A346508 Positive integers k such that 10*k+1 is equal to the product of two integers greater than 1 and ending with 1 (A346507).

12, 23, 34, 44, 45, 56, 65, 67, 78, 86, 89, 96, 100, 107, 111, 122, 127, 128, 133, 144, 149, 155, 158, 166, 168, 170, 177, 188, 189, 191, 199, 209, 210, 212, 220, 221, 232, 233, 243, 250, 251, 254, 260, 265, 275, 276, 282, 287, 291, 296, 298, 309, 311, 313, 317

Offset

1,1

Links

Stefano Spezia, Table of n, a(n) for n = 1..10000

Formula

a(n) = (A346507(n) - 1)/10.

Conjecture: lim_{n->infinity} a(n)/a(n-1) = 1.

The conjecture is true since a(n) = (A346507(n) - 1)/10 and lim_{n->infinity} A346507(n)/A346507(n-1) = 1. - Stefano Spezia, Aug 21 2021

Example

107 is a term because 21*51 = 1071 = 107*10 + 1.

Mathematica

a={}; For[n=1, n<=350, n++, For[k=1, k<n, k++, If[Mod[10n+1, 10k+1]==0 && Mod[(10n+1)/(10k+1), 10]==1 && 10n+1>Max[10a+1], AppendTo[a, n]]]]; a

Prog

(Python)
def aupto(lim): return sorted(set(a*b//10 for a in range(11, 10*lim//11+2, 10) for b in range(a, 10*lim//a+2, 10) if a*b//10 <= lim))
print(aupto(318)) # Michael S. Branicky, Aug 21 2021

Crossrefs

Cf. A016873 (ending with 5), A017281, A324298 (ending with 6), A346507, A346509, A346510.

Sequence in context: A048992 A088783 A029756 * A104340 A367362 A136414

Adjacent sequences: A346505 A346506 A346507 * A346509 A346510 A346511

Keyword

nonn,base

Author

Stefano Spezia, Jul 21 2021

Status

approved