A347747 Positive integers with final digit 6 that are equal to the product of two integers ending with the same digit.
16, 36, 56, 96, 136, 156, 176, 196, 216, 256, 276, 296, 336, 376, 396, 416, 456, 476, 496, 516, 536, 576, 616, 636, 656, 676, 696, 736, 756, 776, 816, 856, 876, 896, 936, 976, 996, 1016, 1036, 1056, 1096, 1116, 1136, 1156, 1176, 1196, 1216, 1236, 1256, 1296, 1316
Offset: 1
Examples
16 = 4*4, 36 = 6*6, 56 = 4*14, 96 = 4*24 = 6*16, 136 = 4*34, 156 = 6*26, ...
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
a={}; For[n=0, n<=150, n++, For[k=0, k<=n, k++, If[Mod[10*n+6, 10*k+4]==0 && Mod[(10*n+6)/(10*k+4), 10]==4 && 10*n+6>Max[a] || 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 tisdQ[n_]:=AnyTrue[{Mod[#,10],Mod[n/#,10]}&/@Divisors[n],#[[1]] == #[[2]]&]; Select[10 Range[150]+6,tisdQ] (* Harvey P. Dale, Dec 27 2021 *) -
PARI
isok(m) = if ((m % 10) == 6, fordiv(m, d, if ((d % 10) == (m/d % 10), return(1)))); \\ Michel Marcus, Oct 06 2021
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Python
def aupto(lim): return sorted(set(a*b for a in range(4, lim//4+1, 10) for b in range(a, lim//a+1, 10)) | set(a*b for a in range(6, lim//6+1, 10) for b in range(a, lim//a+1, 10))) print(aupto(1317)) # Michael S. Branicky, Sep 12 2021
Formula
Lim_{n->infinity} a(n)/a(n-1) = 1.
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