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A260674 Primes p for which the greatest common divisor of 2^p+1 and 3^p+1 is greater than 1. 1
2, 83, 107, 367, 569, 887, 1327, 1451, 1621, 1987, 2027, 3307, 3547, 3631, 3691, 4421, 4547, 4967, 5669, 5843, 5927, 6011, 6911, 6991, 7207, 7949, 8167, 8431, 10771, 10889, 11287, 11621, 12007, 12227, 12487, 12763, 12983, 15391, 15767, 16127, 17107, 17183, 17231 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes p such that A066803(p)>1. - Tom Edgar, Nov 15 2015

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..1000

EXAMPLE

Since GCD(2^83 + 1, 3^83 + 1) = 499, the prime 83 is in the sequence. It is only the second such prime, so a(2) = 83.

MATHEMATICA

Select[Prime@ Range@ 2000, GCD[2^# + 1, 3^# + 1] > 1 &] (* Michael De Vlieger, Nov 16 2015 *)

PROG

(Sage/Python)

# code will list all such primes no larger than the N-th prime.

N=1000

for k in range(N):

if (gcd(2^Primes().unrank(k)+1, 3^Primes().unrank(k)+1) != 1):

print(Primes().unrank(k))

(PARI) list(lim)=forprime(p=2, lim, if(gcd(2^p+1, 3^p+1)>1, print1(p, ", "))) \\ Anders Hellström, Nov 14 2015

(Python)

from sympy import prime

from fractions import gcd

A260674_list = [p for p in (prime(n) for n in range(1, 10**3)) if gcd(2**p+1, 3**p+1) > 1] # Chai Wah Wu, Nov 23 2015

CROSSREFS

Cf. A066803.

Sequence in context: A140157 A285689 A139867 * A090434 A062603 A007353

Adjacent sequences:  A260671 A260672 A260673 * A260675 A260676 A260677

KEYWORD

nonn

AUTHOR

Alex Jordan, Nov 14 2015

STATUS

approved

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Last modified December 15 22:02 EST 2019. Contains 330012 sequences. (Running on oeis4.)