A275415 Pairs of primes (p, q) such that |2p - 3q| = 1.

5, 3, 7, 5, 11, 7, 17, 11, 19, 13, 29, 19, 43, 29, 47, 31, 61, 41, 71, 47, 79, 53, 89, 59, 101, 67, 107, 71, 109, 73, 151, 101, 163, 109, 191, 127, 197, 131, 223, 149, 227, 151, 251, 167, 269, 179, 271, 181, 317, 211, 349, 233, 359, 239, 421, 281, 439, 293

Offset: 1

Author

Michel Lagneau, Aug 09 2016

Keywords

• nonn

Comments

We observe that a(2n-1) = A265761(n+1) and a(2n) = A222565(n+1).

Examples

			The first pair (5, 3) is in the sequence because |2*5 - 3*3| = 1;
The second pair (7, 5) is in the sequence because |2*7 - 3*5|= 1.
		

Crossrefs

Cf. A222565, A265761.

Programs

Maple

nn:=100:for i from 3 to nn do:
p:=ithprime(i):r:=irem(p,3):q:=(2*p + (-1)^(r+1))/3:
  if isprime(q)
   then
  printf(`%d, `,p): printf(`%d, `,q):
  else
  fi:
od:

PARI

lista(n)=forprime(i=3,n,j=(1.5*i)\1;j+=((j+1)%2);if(isprime(j),print1(j", "i", "))) \\ David A. Corneth, Aug 09 2016