

A226542


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


2



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
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OFFSET

1,1


COMMENTS

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


LINKS



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



KEYWORD

nonn,base


AUTHOR



STATUS

approved



