A169605 Numbers x of the form x = 2*y - 3 = 3*z - 2 where y and z are primes.

7, 19, 31, 55, 91, 139, 175, 199, 211, 379, 391, 451, 499, 535, 631, 715, 919, 931, 1039, 1135, 1291, 1315, 1399, 1435, 1639, 1711, 1759, 1819, 1855, 1891, 1939, 2179, 2215, 2359, 2431, 2515, 2575, 2719, 2731, 2899, 2971, 3115, 3271, 3691, 3775, 3955, 4195

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 03 2009

Keywords

• nonn

Examples

			a(1)=7 because 5*2 - 3 = 3*3 - 2;
a(2)=19 because 11*2 - 3 = 7*3 - 2.
		

Crossrefs

Cf. A000040, A131426.

Programs

Maple

isA169605 := proc(x) if type(x+3,'even') then if (x+2) mod 3 = 0 then isprime( (x+3)/2) and isprime((x+2)/3) ; else false ; end if else false; end if; end proc: for x from 1 to 10000 do if isA169605(x) then printf("%d,",x) ; end if; end do: # R. J. Mathar, Jan 27 2010

Mathematica

Select[3Prime[Range[250]]-2,PrimeQ[(3+#)/2]&] (* Harvey P. Dale, May 11 2011 *)

Sage

is_prime_Q = lambda x: x.is_integral() and Integer(x).is_prime()
A169605 = list(x for x in range(1, 10**4) if is_prime_Q((x+3)/2) and
is_prime_Q((x+2)/3))
A169605[:36]
# D. S. McNeil, Dec 21 2009

Extensions

Corrected and extended by Jim Nastos and D. S. McNeil, Dec 21 2009

A few more terms from R. J. Mathar, Jan 27 2010