A348544 Positive integers that are equal both to the product of two integers ending with 3 and to that of two integers ending with 7.

189, 399, 459, 609, 729, 819, 969, 999, 1029, 1239, 1269, 1449, 1479, 1539, 1659, 1729, 1809, 1869, 1989, 2079, 2109, 2289, 2349, 2499, 2619, 2639, 2679, 2709, 2889, 2919, 3009, 3059, 3129, 3159, 3219, 3249, 3339, 3429, 3519, 3549, 3699, 3759, 3819, 3969, 4029

Offset

1,1

Comments

Intersection of A346950 and A348054.

Links

Table of n, a(n) for n=1..45.

Formula

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

Example

189 = 7*27 = 3*63, 399 = 3*133 = 7*57, 459 = 3*153 = 17*27, 609 = 3*203 = 7*87, ...

Mathematica

max=4050; Select[Intersection[Union@Flatten@Table[a*b, {a, 3, Floor[max/3], 10}, {b, a, Floor[max/a], 10}], Union@Flatten@Table[a*b, {a, 7, Floor[max/7], 10}, {b, a, Floor[max/a], 10}]], 0<#<max&]

Prog

(PARI) isok(m) = my(ok3=0, ok7=0); fordiv(m, d, if (((d % 10) == 3) && ((m/d % 10) == 3), ok3++); if (((d % 10) == 7) && ((m/d % 10) == 7), ok7++); if (ok3 && ok7, return(1))); \\ 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(4029)) # Michael S. Branicky, Oct 22 2021

Crossrefs

Cf. A017377 (supersequence), A346950, A348054, A348546.

Sequence in context: A320709 A224674 A076759 * A211815 A347390 A292173

Adjacent sequences: A348541 A348542 A348543 * A348545 A348546 A348547

Keyword

nonn,base

Author

Stefano Spezia, Oct 22 2021

Status

approved