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

1,1

Comments

Union of A346950 and A348054.

Links

Table of n, a(n) for n=1..54.

Formula

Lim_{n->infinity} a(n)/a(n-1) = 1.

Example

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, ...

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

Prog

(PARI) isok(m) = ((m%10) == 9) && sumdiv(m, d, (d % 10) == (m/d % 10)); \\ Michel Marcus, Oct 22 2021
(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

Crossrefs

Cf. A017377 (supersequence), A346950, A348054, A348547.

Sequence in context: A343521 A050854 A053181 * A346950 A192608 A158447

Adjacent sequences: A348542 A348543 A348544 * A348546 A348547 A348548

Keyword

nonn,base

Author

Stefano Spezia, Oct 22 2021

Status

approved