A227072 Positive numbers with nondecreasing digits such that sum of cubes of the digits equals the square of the sum of the digits.

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.

Links

T. D. Noe, Table of n, a(n) for n = 1..660

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

Adjacent sequences: A227069 A227070 A227071 * A227073 A227074 A227075

Keyword

nonn,base,fini,full

Author

T. D. Noe, Jul 27 2013

Status

approved