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
Since A161509 has terms of varying magnitude, sorting any finite initial segment of A161509 cannot provide a guarantee that there are no other terms missed in between. Any prime p not (yet) appearing in A161509 should be tested via A064078(A002326((p-1)/2))=p to conclude whether it belongs to the current sequence. - Max Alekseyev, Feb 10 2024
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 *)
PROG
(PARI) { is_a144755(p) = my(q, m, g); q=znorder(Mod(2, p)); m=2^q-1; fordiv(q, d, if(d<q, while((g=gcd(m, 2^d-1))>1, m\=g))); m==p; } \\ Max Alekseyev, Feb 10 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 20 2008
EXTENSIONS
Extended by T. D. Noe, Apr 13 2010
b-file deleted by Max Alekseyev, Feb 10 2024.
STATUS
approved