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A227072
Positive numbers with nondecreasing digits such that sum of cubes of the digits equals the square of the sum of the digits.
3
1, 12, 22, 123, 333, 1224, 1234, 2244, 4444, 12235, 12345, 33336, 33346, 55555, 111225, 111445, 112455, 114555, 122346, 122446, 123456, 144466, 222226, 224466, 244557, 244666, 333357, 333666, 345567, 355567, 455667, 666666, 1122556, 1134457, 1145557, 1155666
OFFSET
1,2
COMMENTS
Because the digits are nondecreasing, the search to 10^20 is fairly rapid.
EXAMPLE
1234 is here because 1^3 + 2^3 + 3^3 + 4^3 = (1 + 2 + 3 + 4)^2 and its digits are nondecreasing..
MATHEMATICA
(* complete sequence *) tx = {}; Do[d = {i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20}; If[Total[d^3] == Total[d]^2, n = FromDigits[d]; AppendTo[tx, n]], {i1, 0, 9}, {i2, i1, 9}, {i3, i2, 9}, {i4, i3, 9}, {i5, i4, 9}, {i6, i5, 9}, {i7, i6, 9}, {i8, i7, 9}, {i9, i8, 9}, {i10, i9, 9}, {i11, i10, 9}, {i12, i11, 9}, {i13, i12, 9}, {i14, i13, 9}, {i15, i14, 9}, {i16, i15, 9}, {i17, i16, 9}, {i18, i17, 9}, {i19, i18, 9}, {i20, i19, 9}]; tx = Rest[tx]
(* partial sequence *) nddQ[n_] := Module[{idn=IntegerDigits[n]}, Min[Differences[idn]] >= 0 && Total[idn^3] == Total[idn]^2]; Select[Range[2000000], nddQ] (* Harvey P. Dale, Sep 01 2013 *)
CROSSREFS
Cf. A225567 (primes in a related sequence), A227073.
Sequence in context: A014633 A298323 A299216 * A066458 A246342 A101104
KEYWORD
nonn,base,fini,full
AUTHOR
T. D. Noe, Jul 27 2013
STATUS
approved