A348054 Positive integers that are the product of two integers ending with 7.

49, 119, 189, 259, 289, 329, 399, 459, 469, 539, 609, 629, 679, 729, 749, 799, 819, 889, 959, 969, 999, 1029, 1099, 1139, 1169, 1239, 1269, 1309, 1369, 1379, 1449, 1479, 1519, 1539, 1589, 1649, 1659, 1729, 1739, 1799, 1809, 1819, 1869, 1939, 1989, 2009, 2079, 2109

Offset: 1

Author

Stefano Spezia, Sep 26 2021

Keywords

• nonn
• base

Examples

			49 = 7*7, 119 = 7*17, 189 = 7*27, 259 = 7*37, 289 = 17*17, 329 = 7*47, 399 = 7*57, ...
		

Crossrefs

Cf. A017377 (supersequence), A053742 (ending with 5), A139245 (ending with 2), A324297 (ending with 6), A346950 (ending with 3), A347253 (ending with 4), A348055.

Programs

Mathematica

a={}; For[n=0, n<=210, n++, For[k=0, k<=n, k++, If[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

Python

def aupto(lim): return sorted(set(a*b for a in range(7, lim//7+1, 10) for b in range(a, lim//a+1, 10)))
print(aupto(2110)) # Michael S. Branicky, Sep 26 2021

Formula

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