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A324297
Positive integers k that are the product of two integers ending with 6.
14
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
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
KEYWORD
nonn,base
AUTHOR
Stefano Spezia, Mar 16 2019
STATUS
approved