A226542 Primes p such that p - 1 can be represented as a repdigit number in some base < p which is a power of two.

11, 19, 37, 43, 67, 103, 131, 137, 199, 239, 293, 331, 397, 439, 463, 521, 547, 661, 683, 727, 859, 911, 991, 1033, 1093, 1171, 1291, 1301, 1543, 1549, 1951, 2053, 2081, 2341, 2731, 2861, 3079, 3121, 3251, 3511, 3613, 3823, 4099, 4129, 4229, 4903, 5419, 6151

Offset: 1

Author

Arkadiusz Wesolowski, Jun 10 2013

Keywords

• nonn
• base

Comments

It is believed that this is a supersequence of A001220 (Wieferich primes).

Examples

			103 is in the sequence because it is prime and 102 = 66 (base 16).
463 is in the sequence because it is prime and 462 = ee (base 32).
7 is not in the sequence since 6 = 6 (base 8) and 8 > 7.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
• John Blythe Dobson, A note on the two known Wieferich Primes
• Wells Johnson, On the nonvanishing of Fermat quotients (mod p), Journal f. die reine und angewandte Mathematik 292, (1977): 196-200.
• Wikipedia, Repdigit

Crossrefs

Cf. A001220, A010785, A048329, A048333, A048340.

Programs

Mathematica

lst = {}; r = 13; Do[If[PrimeQ[p] && Length@Union@IntegerDigits[p - 1, 2^b] == 1, AppendTo[lst, p]], {b, 2, r - 1}, {p, 2^b + 1, 2^r - 1, 2}]; Union[lst]