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A324298
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Positive integers k such that 10*k+6 is equal to the product of two integers ending with 6 (A324297).
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7
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3, 9, 15, 21, 25, 27, 33, 39, 41, 45, 51, 57, 63, 67, 69, 73, 75, 81, 87, 89, 93, 99, 105, 111, 117, 119, 121, 123, 129, 135, 137, 141, 145, 147, 153, 159, 165, 169, 171, 177, 183, 185, 189, 195, 197, 201, 207, 211, 213, 217, 219, 223, 225, 231, 233, 237, 243, 249
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OFFSET
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1,1
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COMMENTS
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All the terms of this sequence are odd.
Why? If an integer 10*k+6 = (10*a+6) * (10*b+6), then k = 10*a*b + 6*(a+b) + 3, so k is odd. - Bernard Schott, May 13 2019
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LINKS
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FORMULA
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Conjecture: lim_{n->infinity} a(n)/a(n-1) = 1.
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EXAMPLE
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145 is a term because 26*56 = 1456 = 145*10 + 6. - Bernard Schott, May 13 2019
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MATHEMATICA
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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[10*a+6], AppendTo[a, n]]]]; a
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PROG
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(PARI) isok6(n) = (n%10) == 6; \\ A017341
isok(k) = {my(n=10*k+6, 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//10 for a in range(6, 10*lim//6+2, 10) for b in range(a, 10*lim//a+2, 10) if a*b//10 <= lim))
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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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