A260906 Numbers n such that 3*n and n^3 have the same digit sum.

0, 3, 6, 30, 60, 63, 126, 171, 252, 300, 324, 543, 585, 600, 630, 1260, 1281, 1710, 2520, 2925, 3000, 3240, 5430, 5850, 5946, 6000, 6300, 12600, 12606, 12633, 12810, 14631, 16263, 17100, 21618, 22308, 22971, 24663, 25200, 27633, 28845, 28887, 28965, 29241

Offset: 1

Author

Vincenzo Librandi, Nov 18 2015

Keywords

• nonn
• base
• easy

Comments

All terms are multiples of 3.

n is in the sequence iff 10*n is. Are there infinitely many terms not divisible by 10? - Robert Israel, Nov 20 2015

Examples

			126 is in the sequence because 126^3 = 2000376 and 3*126 = 378 have the same digit sum: 18.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..320

Crossrefs

Cf. A000578, A007953, A008585, A049343, A260702.

Programs

Magma

[n: n in [0..50000] | &+Intseq(3*n) eq &+Intseq(n^3)];

Maple

select(n -> convert(convert(n^3,base,10),`+`)=convert(convert(3*n,base,10),`+`), 3*[$0..10^5]); # Robert Israel, Nov 20 2015

Mathematica

Select[Range[0, 50000], Total[IntegerDigits[3 #]] == Total[IntegerDigits[#^3]] &]

PARI

for(n=0, 1e5, if(sumdigits(n^3)==sumdigits(3*n), print1(n, ", "))) \\ Altug Alkan, Nov 20 2015

Formula

A007953(A008585(a(n))) = A007953(A000578(a(n))).