A167996 Positive numbers n with property that first digit of 3*n = last digit of n.

13, 14, 28, 41, 51, 61, 72, 82, 92, 103, 113, 123, 133, 134, 144, 154, 164, 175, 185, 195, 206, 216, 226, 237, 247, 257, 268, 278, 288, 298, 309, 319, 329, 341, 351, 361, 371, 381, 391, 401, 411, 421, 431, 441, 451, 461, 471, 481, 491, 501, 511, 521, 531, 541, 551, 561, 571, 581

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

A000030(A008585(a(n))) = A010879(a(n)). (Defining property of the terms of this sequence.) - M. F. Hasler, Apr 22 2024

Example

3*13=39, 3*14=42, 3*28=84, 3*41=123, etc.

Mathematica

Reap[Do[If[IntegerDigits[n][[ -1]]==IntegerDigits[3*n][[1]], Sow[n]], {n, 1000}]][[2, 1]]
Select[Range[600], Last[IntegerDigits[#]]==First[IntegerDigits[3#]]&] (* Harvey P. Dale, Jul 10 2013 *)

Prog

(PARI) select( {is_A167996(n)=n*3\10^logint(3*n+!n, 10)==n%10}, [1..666]) \\ M. F. Hasler, Apr 22 2024
(Python) is_A167996 = lambda x: int(str(3*x)[0]) == x % 10 # M. F. Hasler, Apr 22 2024

Crossrefs

Cf. A000030 (first digit of n), A010879 (last digit of n), A008585 (3*n).

Cf. A167994.

Sequence in context: A041340 A041338 A042411 * A308122 A292116 A071870

Adjacent sequences: A167993 A167994 A167995 * A167997 A167998 A167999

Keyword

base,nonn

Author

Zak Seidov, Nov 16 2009

Status

approved