A324297 Positive integers k that are the product of two integers ending with 6.

36, 96, 156, 216, 256, 276, 336, 396, 416, 456, 516, 576, 636, 676, 696, 736, 756, 816, 876, 896, 936, 996, 1056, 1116, 1176, 1196, 1216, 1236, 1296, 1356, 1376, 1416, 1456, 1476, 1536, 1596, 1656, 1696, 1716, 1776, 1836, 1856, 1896, 1956, 1976, 2016, 2076, 2116

Offset

1,1

Comments

All the terms end with 6 (A017341).

Links

Stefano Spezia, Table of n, a(n) for n = 1..10000

Formula

Conjecture: Lim_{n->infinity} a(n)/a(n-1) = 1.

The conjecture is true since it can be proved that a(n) = (sqrt(a(n-1)) + g(n-1))^2 where [g(n): n > 1] is a bounded sequence of positive real numbers. - Stefano Spezia, Aug 18 2021

Example

36 = 6*6, 96 = 6*16, 216 = 6*36, 256 = 16*16, 276 = 6*46, ...

Mathematica

a={}; For[n=0, n<=250, n++, For[k=0, k<=n, k++, If[Mod[10*n+6, 10*k+6]==0 && Mod[(10*n+6)/(10*k+6), 10]==6 && 10*n+6>Max[a], AppendTo[a, 10*n+6]]]]; a

Prog

(PARI) isok6(n) = (n%10) == 6; \\ A017341
isok(n) = {if (isok6(n), my(d=divisors(n)); fordiv(n, d, if (isok6(d) && isok6(n/d), return(1))); ); return (0); } \\ Michel Marcus, Apr 14 2019
(Python)
def aupto(lim): return sorted(set(a*b for a in range(6, lim//6+1, 10) for b in range(a, lim//a+1, 10)))
print(aupto(2117)) # Michael S. Branicky, Aug 18 2021

Crossrefs

Cf. A000400, A017341 (supersequence), A324298, A053742 (ending with 5).

Sequence in context: A247246 A242238 A200866 * A250785 A057392 A287613

Adjacent sequences: A324294 A324295 A324296 * A324298 A324299 A324300

Keyword

nonn,base

Author

Stefano Spezia, Mar 16 2019

Status

approved