A375257 Numbers whose sum of base-2 digits is 1 more than their sum of base-3 digits.

3, 9, 15, 28, 29, 39, 45, 57, 82, 83, 84, 85, 94, 95, 99, 110, 118, 119, 123, 135, 162, 163, 165, 174, 175, 183, 207, 219, 248, 297, 303, 315, 324, 325, 334, 335, 342, 343, 363, 382, 383, 406, 407, 411, 423, 435, 441, 447, 459, 488, 494, 496, 497, 502, 503, 506, 508, 509, 543, 570, 571, 573, 603

Offset

1,1

Comments

Numbers k such that A000120(k) = A053735(k) + 1.

Links

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

Example

a(3) = 15 is a term because 15 = 1111_2 = 120_3 so A000120(15) = 1+1+1+1 = 4 and A053735(15) = 1+2+0 = 3.

Maple

filter:= proc(n) convert(convert(n, base, 2), `+`) = convert(convert(n, base, 3), `+`)+1 end proc:
select(filter, [$1..1000]);

Mathematica

Select[Range[600], Subtract @@ DigitSum[#, {2, 3}] == 1 &] (* Amiram Eldar, Aug 08 2024 *)

Prog

(Python)
from sympy.ntheory import digits
def ok(n): return sum(digits(n, 2)[1:]) == sum(digits(n, 3)[1:]) + 1
print([k for k in range(604) if ok(k)]) # Michael S. Branicky, Aug 08 2024
(PARI) isok(k) = sumdigits(k, 2) == 1 + sumdigits(k, 3); \\ Michel Marcus, Aug 08 2024

Crossrefs

Cf. A000120, A037301, A053735, A180017.

Sequence in context: A280963 A122819 A056287 * A099409 A002127 A357764

Adjacent sequences: A375254 A375255 A375256 * A375258 A375259 A375260

Keyword

nonn,base

Author

Robert Israel, Aug 07 2024

Status

approved