A260702 Numbers n such that 3*n and n^2 have the same digit sum.

0, 3, 6, 9, 12, 15, 18, 21, 30, 33, 39, 45, 48, 51, 60, 66, 90, 96, 99, 102, 105, 111, 120, 123, 129, 132, 150, 153, 156, 159, 162, 165, 180, 189, 195, 198, 201, 210, 225, 231, 246, 252, 255, 261, 285, 300, 330, 333, 348, 351, 390, 399, 429, 450, 453, 459, 462

Offset: 1

Author

Vincenzo Librandi, Nov 17 2015

Keywords

• nonn
• base
• easy

Comments

All terms are multiple of 3.

If n is in the sequence, then so is 10*n. - Robert Israel, Apr 05 2020

Examples

			159 is in the sequence because 159^2 = 25281 and 3*159 = 477 have the same digit sum: 18.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A007953, A008585, A049343, A058369.

Contains A133384 and A199682.

Programs

Magma

[n: n in [0..500] | &+Intseq(3*n) eq &+Intseq(n^2)];

Maple

select(n -> convert(convert(3*n,base,10),`+`)=convert(convert(n^2,base,10),`+`), [seq(i,i=0..1000,3)]); # Robert Israel, Apr 05 2020

Mathematica

Select[Range[0, 500], Total[IntegerDigits[3 #]] == Total[IntegerDigits[#^2]] &]

PARI

isok(n) = sumdigits(3*n) == sumdigits(n^2); \\ Michel Marcus, Nov 17 2015

Sage

[n for n in (0..500) if sum((3*n).digits())==sum((n^2).digits())] # Bruno Berselli, Nov 17 2015

Formula

A007953(A008585(a(n))) = A007953(A000290(a(n))).