A172365 List of primes p1, p2 and p3 such that 3*p1 - 2 = 2*p2 - 3 = p3.

3, 5, 7, 7, 11, 19, 11, 17, 31, 47, 71, 139, 67, 101, 199, 71, 107, 211, 127, 191, 379, 167, 251, 499, 211, 317, 631, 307, 461, 919, 347, 521, 1039, 431, 647, 1291, 467, 701, 1399, 587, 881, 1759, 727, 1091, 2179, 907, 1361, 2719, 911, 1367, 2731, 991, 1487, 2971

Offset: 1

Author

Juri-Stepan Gerasimov, Feb 01 2010

Keywords

• nonn

Examples

			a(1) = 3 = p1, a(2) = 5 = p2, a(3) = 7 = p3 because 3*3 - 2 = 2*5 - 3 = 7;
a(4) = 11 = p1, a(5) = 17 = p2, a(6) = 31 = p3 because 3*11 - 2 = 2*17 - 3 = 31.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A000040, A172287, A172888.

Programs

Maple

for n from 1 to 500 do p1 := ithprime(n) ; p3 := 3*p1-2 ; if isprime(p3) then p2 := (p3+3)/2 ; if isprime(p2) then printf("%d,%d,%d,",p1,p2,p3) ; end if; end if; end do: # R. J. Mathar, May 02 2010

Mathematica

Flatten[Select[Tuples[Prime[Range[450]],{3}],3First[#]-2==2#[[2]]-3== Last[#]&]] (* Harvey P. Dale, Jun 02 2011 *)

Extensions

Corrected (triples 7,11,19 and 167,251,499 inserted) and extended by R. J. Mathar, May 02 2010