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A226542 Primes p such that p - 1 can be represented as a repdigit number in some base < p which is a power of two. 1
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 (list; graph; refs; listen; history; text; internal format)
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 A271779 A271840

Adjacent sequences:  A226539 A226540 A226541 * A226543 A226544 A226545

KEYWORD

nonn,base

AUTHOR

Arkadiusz Wesolowski, Jun 10 2013

STATUS

approved

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Last modified January 24 04:31 EST 2018. Contains 298115 sequences.