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

1,2

Comments

All terms are multiple of 3.

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

Links

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

Formula

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

Example

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

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]] &]

Prog

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

Crossrefs

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

Contains A133384 and A199682.

Sequence in context: A329844 A127451 A022844 * A262712 A195934 A195933

Adjacent sequences: A260699 A260700 A260701 * A260703 A260704 A260705

Keyword

nonn,base,easy

Author

Vincenzo Librandi, Nov 17 2015

Status

approved