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A347747
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Positive integers with final digit 6 that are equal to the product of two integers ending with the same digit.
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2
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Lim_{n->infinity} a(n)/a(n-1) = 1.
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EXAMPLE
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16 = 4*4, 36 = 6*6, 56 = 4*14, 96 = 4*24 = 6*16, 136 = 4*34, 156 = 6*26, ...
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MATHEMATICA
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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 *)
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PROG
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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)))
(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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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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