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

Author

T. D. Noe, Jul 27 2013

Keywords

• nonn
• base
• fini
• full

Comments

Because the digits are nondecreasing, the search to 10^20 is fairly rapid.

Examples

			1234 is here because 1^3 + 2^3 + 3^3 + 4^3 = (1 + 2 + 3 + 4)^2 and its digits are nondecreasing..
		

Links

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

Crossrefs

Cf. A225567 (primes in a related sequence), A227073.

Programs

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 *)