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A144755 Primes which divide none of overpseudoprimes to base 2 (A141232). 8
2, 3, 5, 7, 11, 13, 17, 19, 31, 41, 43, 73, 127, 151, 241, 257, 331, 337, 683, 2731, 5419, 8191, 43691, 61681, 65537, 87211, 131071, 174763, 262657, 524287, 599479, 2796203, 15790321, 18837001, 22366891, 715827883, 2147483647, 4278255361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Odd prime p is in the sequence iff A064078(A002326((p-1)/2))=p. For example, for p=127 we have A002326((127-1)/2)=7 and A064078(7)=127. Thus p=127 is in the sequence.

Primes p such that the binary expansion of 1/p has a unique period length; that is, no other prime has the same period. Sequence A161509 sorted. - T. D. Noe, Apr 13 2010

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..97

EXAMPLE

Overpseudoprimes to base 2 are odd, then a(1)=2.

MATHEMATICA

b=2; t={}; Do[c=Cyclotomic[n, b]; q=c/GCD[n, c]; If[PrimePowerQ[q], p=FactorInteger[q][[1, 1]]; If[p<10^12, AppendTo[t, p]; Print[{n, p}]]], {n, 1000}]; t=Sort[t] (* T. D. Noe, Apr 13 2010 *)

CROSSREFS

Cf. A141232, A002326, A064078, A112927.

Cf. A040017 (unique-period primes in base 10). - T. D. Noe, Apr 13 2010

Sequence in context: A181561 A216496 A069709 * A069090 A321150 A088415

Adjacent sequences:  A144752 A144753 A144754 * A144756 A144757 A144758

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Sep 20 2008

EXTENSIONS

Extended by T. D. Noe, Apr 13 2010

STATUS

approved

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Last modified August 18 15:00 EDT 2019. Contains 326106 sequences. (Running on oeis4.)