Exponential digital sums: Difference between revisions

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 * Find and show at least the first ten integers with their exponents, that satisfy this condition in three or more ways.
+=={{header|Julia}}==
+<syntaxhighlight lang="julia">function equal_digitalsum_exponents(n::Integer)
+    equalpows = Int[]
+    if n > 1
+        npow, misses = 2, 0
+        while misses < n + 50
+            dsum = sum(digits(BigInt(n) ^ npow))
+            if npow > 10 && dsum > 2 * n
+                break # bail here for time contraints (see Wren example)
+            elseif dsum == n
+                push!(equalpows, npow)
+            else
+                misses += 1
+            end
+            npow += 1
+        end
+    end
+    return equalpows
+end
+function testdigitalequals(lim, wanted, multiswanted)
+    found1, found2, multis = 0, 0, Tuple{Int, Vector{Int}}[]
+    println("First $wanted integers that are equal to the digital sum of that integer raised to some power:")
+    for i in 1:lim
+        a = equal_digitalsum_exponents(i)
+        if !isempty(a)
+            found1 += 1
+            if found1 <= wanted
+                print(rpad(i, 6), found1 % 10 == 0 ? "\n" : "")
+            end
+            if length(a) > 2
+                found2 += 1
+                push!(multis, (i, a))
+                if found2 == multiswanted
+                    println("\nFirst $multiswanted that satisfy that condition in three or more ways:")
+                    for (n, v) in multis
+                        println("$n: powers $v")
+                    end
+                    break
+                end
+            end
+        end
+    end
+end
+testdigitalequals(6000, 25, 30)
+<syntaxhighlight>{{out}}
+<pre>
+First 25 integers that are equal to the digital sum of that integer raised to some power:
+8     9     17    18    20    22    25    26    27
+31    34    35    36    40    43    45    46    53
+58    63    64    68
+First 30 that satisfy that condition in three or more ways:
+: powers [3, 6, 7]
+: powers [6, 8, 9]
+: powers [19, 20, 21, 22, 28]
+: powers [11, 13, 15]
+: powers [16, 18, 19, 20]
+: powers [45, 46, 49, 51]
+: powers [48, 54, 57, 59]
+: powers [32, 35, 36]
+: powers [39, 42, 44, 45]
+: powers [44, 47, 54]
+: powers [48, 54, 58]
+: powers [57, 60, 64]
+: powers [72, 77, 81]
+: powers [78, 80, 82, 86]
+: powers [92, 98, 102]
+: powers [121, 126, 131]
+: powers [123, 127, 132]
+: powers [140, 143, 147]
+: powers [213, 215, 229]
+: powers [217, 222, 223, 229, 230]
+: powers [161, 166, 174]
+: powers [228, 244, 246]
+: powers [170, 172, 176]
+: powers [406, 414, 420, 427]
+: powers [177, 189, 190]
+: powers [191, 193, 195]
+: powers [187, 193, 199]
+: powers [189, 202, 210]
+: powers [203, 207, 209]
+: powers [215, 221, 227]
+</pre>