

A122095


Primes p for which 8*p+1 divides 2^p1.


2



11, 29, 179, 239, 431, 761, 857, 941, 1367, 1667, 1871, 1877, 2411, 2837, 3041, 3119, 3329, 3347, 3767, 4289, 5021, 5087, 5231, 5261, 5717, 5861, 6449, 6917, 6959, 7079, 7211, 7919, 8429, 8741, 8867, 9341, 9461, 9851, 10211, 10979, 12107, 12437, 12479
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OFFSET

1,1


COMMENTS

The first 962 terms, all those with n<500000, are also in A023228.  R. J. Mathar, Oct 20 2006
All terms are in A023228, i.e., such that 8p+1 is prime, since a divisor of 8p+1 would also divide M(p)=A000225(p) and thus be of the form 2kp+1, but it is easily checked that 8p+1 cannot be a multiple of 2p+1 (nor of 4p+1 or 6p+1, of course).  M. F. Hasler, Mar 21 2011


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000


EXAMPLE

29 is in this sequence because 2^291 is divisible by 8 * 29 + 1 = 233.


MAPLE

isA122095 := proc(n) RETURN( isprime(n) and ( (2^n1) mod (8*n+1)) = 0 ) ; end: n := 1 : for a from 2 to 500000 do if isA122095(a) then print(n, a) ; n := n+1 ; fi ; od ; # R. J. Mathar, Oct 20 2006


MATHEMATICA

Select[Prime[Range[1500]], Divisible[2^#1, 8#+1]&] (* Harvey P. Dale, Dec 18 2012 *)
Select[Prime[Range[1500]], PowerMod[2, #, 8#+1]==1&] (* Harvey P. Dale, May 28 2015 *)


PROG

(PARI) forprime( p=1, 1e4, Mod(2, p*8+1)^p1  print1(p", "))


CROSSREFS

Cf. A000225, A002515, A188130.
Sequence in context: A115972 A099109 A302091 * A282137 A027758 A285992
Adjacent sequences: A122092 A122093 A122094 * A122096 A122097 A122098


KEYWORD

nonn


AUTHOR

J. Lowell, Oct 17 2006


EXTENSIONS

More terms from R. J. Mathar, Oct 20 2006


STATUS

approved



