A348545 Positive integers with final digit 9 that are equal to the product of two integers ending with the same digit.
9, 39, 49, 69, 99, 119, 129, 159, 169, 189, 219, 249, 259, 279, 289, 299, 309, 329, 339, 369, 399, 429, 459, 469, 489, 519, 529, 539, 549, 559, 579, 609, 629, 639, 669, 679, 689, 699, 729, 749, 759, 789, 799, 819, 849, 879, 889, 909, 939, 949, 959, 969, 989, 999
Offset: 1
Examples
9 = 3*3, 39 = 3*13, 49 = 7*7, 69 = 3*23, 99 = 3*33, 119 = 7*17, 129 = 3*43, 159 = 3*53, 169 = 13*13, 189 = 3*63 = 7*27, ...
Programs
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Mathematica
a={}; For[n=0, n<=100, n++, For[k=0, k<=n, k++, If[Mod[10*n+9, 10*k+3]==0 && Mod[(10*n+9)/(10*k+3), 10]==3 && 10*n+9>Max[a] || Mod[10*n+9, 10*k+7]==0 && Mod[(10*n+9)/(10*k+7), 10]==7 && 10*n+9>Max[a], AppendTo[a, 10*n+9]]]]; a -
PARI
isok(m) = ((m%10) == 9) && sumdiv(m, d, (d % 10) == (m/d % 10)); \\ Michel Marcus, Oct 22 2021
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Python
def aupto(lim): return sorted(set(a*b for a in range(3, lim//3+1, 10) for b in range(a, lim//a+1, 10)) | set(a*b for a in range(7, lim//7+1, 10) for b in range(a, lim//a+1, 10))) print(aupto(999)) # Michael S. Branicky, Oct 22 2021
Formula
Lim_{n->infinity} a(n)/a(n-1) = 1.
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