A337139 Indices m of repunits R_m that are not Colombian (or self) numbers.

2, 3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77

Offset: 1

Author

Michel Marcus, Aug 19 2020

Keywords

• nonn
• base

Comments

Note that 2, 19, 23, 317, 1031, 49081, 86453, 109297, 270343, 5794777, 8177207 (see A004023) are terms. [Last 2 terms added by Serge Batalov, Aug 24 2021]

While all currently known A004023 terms are in this sequence, there is no clear argument that it would hold for all future values. - Serge Batalov, Aug 24 2021

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002275 (repunits), A004022 (repunit primes), A004023 (indices of repunit primes), A176995 (not Colombian).

Cf. A337208 (complement).

Programs

PARI

upto(n)= {my(res = List()); for(i = 1, n, if(is(i), listput(res, i); print1(i", "))); res}
is(n) = {if(n < 8, return(isprime(n))); qd = n; n = 10^n\9; r = 1 + (n-1)%9; h = (r + 9 * (r%2))/2; ld = 10; while(h + 9*qd >= n % ld, ld*=10); vs = qd - valuation(ld, 10); n %= ld; for(i = 0, qd, if(vs + vecsum(digits(n - h - 9*i)) == h + 9*i, return(1))); 0} \\ David A. Corneth, Aug 20 2020