A171566 Primes p such that 2*p-3 and 2*(2*p-3)-3 are primes (First member of a primes in a 2*p-3 double progression).

3, 5, 7, 13, 17, 23, 37, 43, 97, 107, 113, 127, 157, 167, 223, 283, 317, 373, 433, 547, 563, 587, 617, 647, 743, 757, 773, 937, 1123, 1277, 1297, 1423, 1483, 1487, 1543, 1583, 1597, 1667, 1697, 1823, 1913, 1933, 1973, 2137, 2143, 2243, 2333, 2437, 2467

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 11 2009

Keywords

• nonn

Examples

			2*3-3=3, 2*5-3=7; 2*7-3=11, 2*7-3=11; 2*11-3=19,..
		

References

• Mohammad K. Azarian, Double Progression, Problem 231, Math Horizons, Vol. 16, Issue 4, April 2009, p. 31. Solution published in Vol. 17, Issue 2, November 2009, p. 32.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A063908

Programs

Mathematica

Select[Prime[Range[7! ]],PrimeQ[2*#-3]&&PrimeQ[2*(2*#-3)-3]&]
Select[Prime[Range[400]],AllTrue[{2#-3,4#-9},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 04 2021 *)