Numbers with prime digits whose sum is 13: Difference between revisions
Numbers with prime digits whose sum is 13 (view source)
Revision as of 08:02, 30 September 2020
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=={{header|Julia}}==
<lang julia>using Combinatorics, Primes
function primedigitsums(targetsum)
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possibles = mapreduce(x -> fill(x, div(targetsum, x)), vcat, [2, 3, 5, 7])
a = map(x -> evalpoly(BigInt(10), x),
mapreduce(x -> unique(collect(permutations(x))), vcat,
unique(filter(x -> sum(x) == targetsum, collect(combinations(possibles))))))
println("There are $(length(a)) prime-digit-only numbers summing to $targetsum : $a")
end
foreach(primedigitsums, [5, 7, 11, 13])
function primedigitcombos(targetsum)
possibles = [2, 3, 5, 7]
found = Vector{Vector{Int}}()
combos = [Int[]]
tempcombos = Vector{Vector{Int}}()
newcombos = Vector{Vector{Int}}()
while !isempty(combos)
for combo in combos, j in possibles
csum = sum(combo) + j
if csum <= targetsum
newcombo = sort!([combo; j])
csum < targetsum && !(newcombo in newcombos) && push!(newcombos, newcombo)
csum == targetsum && !(newcombo in found) && push!(found, newcombo)
end
▲ end
empty!(combos)
tempcombos = combos
combos = newcombos
newcombos = tempcombos
▲ end
return found
end
function countprimedigitsums(targetsum)
found = primedigitcombos(targetsum)
total = sum(arr -> factorial(BigInt(length(arr))) ÷
prod(x -> factorial(BigInt(count(y -> y == x, arr))), unique(arr)), found)
println("There are $total prime-digit-only numbers summing to $targetsum.")
end
foreach(countprimedigitsums, nextprimes(17, 40))
</lang>{{out}}
<pre>
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There are 19 prime-digit-only numbers summing to 11 : [722, 272, 227, 533, 353, 335, 5222, 2522, 2252, 2225, 3332, 3323, 3233, 2333, 32222, 23222, 22322, 22232, 22223]
There are 43 prime-digit-only numbers summing to 13 : [733, 373, 337, 553, 535, 355, 7222, 2722, 2272, 2227, 5332, 3532, 3352, 5323, 3523, 5233, 2533, 3253, 2353, 3325, 3235, 2335, 52222, 25222, 22522, 22252, 22225, 33322, 33232, 32332, 23332, 33223, 32323, 23323, 32233, 23233, 22333, 322222, 232222, 223222, 222322, 222232, 222223]
There are 221 prime-digit-only numbers summing to 17.
There are 468 prime-digit-only numbers summing to 19.
There are 2098 prime-digit-only numbers summing to 23.
There are 21049 prime-digit-only numbers summing to 29.
There are 45148 prime-digit-only numbers summing to 31.
There are 446635 prime-digit-only numbers summing to 37.
There are 2061697 prime-digit-only numbers summing to 41.
There are 4427752 prime-digit-only numbers summing to 43.
There are 20424241 prime-digit-only numbers summing to 47.
There are 202405001 prime-digit-only numbers summing to 53.
There are 2005642061 prime-digit-only numbers summing to 59.
There are 4307930784 prime-digit-only numbers summing to 61.
There are 42688517778 prime-digit-only numbers summing to 67.
There are 196942068394 prime-digit-only numbers summing to 71.
There are 423011795680 prime-digit-only numbers summing to 73.
There are 4191737820642 prime-digit-only numbers summing to 79.
There are 19338456915087 prime-digit-only numbers summing to 83.
There are 191629965405641 prime-digit-only numbers summing to 89.
There are 4078672831913824 prime-digit-only numbers summing to 97.
There are 18816835854129198 prime-digit-only numbers summing to 101.
There are 40416663565084464 prime-digit-only numbers summing to 103.
There are 186461075642340151 prime-digit-only numbers summing to 107.
There are 400499564627237889 prime-digit-only numbers summing to 109.
There are 1847692833654336940 prime-digit-only numbers summing to 113.
There are 389696778451488128521 prime-digit-only numbers summing to 127.
There are 1797854500757846669066 prime-digit-only numbers summing to 131.
There are 17815422682488317051838 prime-digit-only numbers summing to 137.
There are 38265729200380568226735 prime-digit-only numbers summing to 139.
There are 1749360471151229472803187 prime-digit-only numbers summing to 149.
There are 3757449669085729778349997 prime-digit-only numbers summing to 151.
There are 37233577041224219717325533 prime-digit-only numbers summing to 157.
There are 368957506121989278337474430 prime-digit-only numbers summing to 163.
There are 1702174484494837917764813972 prime-digit-only numbers summing to 167.
There are 16867303726643249517987636148 prime-digit-only numbers summing to 173.
There are 167142638782573042636172836062 prime-digit-only numbers summing to 179.
There are 359005512666242240589945886415 prime-digit-only numbers summing to 181.
There are 16412337250779890525195727788488 prime-digit-only numbers summing to 191.
There are 35252043354611887665339338710961 prime-digit-only numbers summing to 193.
There are 162634253887997896351270835136345 prime-digit-only numbers summing to 197.
There are 349321957098598244959032342621956 prime-digit-only numbers summing to 199.
</pre>
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