A348544 - OEIS

%I #11 Oct 23 2021 00:08:08

%S 189,399,459,609,729,819,969,999,1029,1239,1269,1449,1479,1539,1659,

%T 1729,1809,1869,1989,2079,2109,2289,2349,2499,2619,2639,2679,2709,

%U 2889,2919,3009,3059,3129,3159,3219,3249,3339,3429,3519,3549,3699,3759,3819,3969,4029

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

%C Intersection of A346950 and A348054.

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

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

%t 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&]

%o (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

%o (Python)

%o 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)))

%o print(aupto(4029)) # _Michael S. Branicky_, Oct 22 2021

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

%K nonn,base

%O 1,1

%A _Stefano Spezia_, Oct 22 2021