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

1,1

Comments

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

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

Example

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.

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]

Crossrefs

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

Sequence in context: A233388 A248398 A052368 * A117873 A321568 A271779

Adjacent sequences: A226539 A226540 A226541 * A226543 A226544 A226545

Keyword

nonn,base

Author

Arkadiusz Wesolowski, Jun 10 2013

Status

approved