A240569 Primes of the form k(m) + k(m+2) where k(m) = A018252(m) (nonprimes), m >= 1.

7, 47, 73, 107, 157, 167, 179, 193, 227, 263, 313, 347, 421, 467, 503, 587, 613, 661, 673, 719, 733, 757, 877, 887, 983, 997, 1019, 1093, 1153, 1187, 1213, 1307, 1367, 1381, 1439, 1453, 1487, 1523, 1753, 1823, 1873, 1907, 1933, 1993, 2017, 2027, 2137, 2207, 2341, 2447, 2473, 2593, 2797

Offset: 1

Author

Ilya Lopatin and Juri-Stepan Gerasimov, Apr 08 2014

Keywords

• nonn
• easy

Comments

This sequence gives the increasingly ordered primes of the form k(m) + k(m+2) with k(m) = A018252(m). The m values are 1, 14, 24, 37, 56, 60, ...

Examples

			a(1) = 7 is the smallest prime of the mentioned form, obtained for m=1: A018252(1) + A018252(3) = 1 + 6 = 7.
a(2) = 47 is the second smallest prime of this form, with m = 14:  A018252(14) + A018252(16) = 22 + 25 = 47.
		

Links

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

Crossrefs

Cf. A018252, A167611.

Programs

Magma

m:=1500; NonPrime:=[i: i in [0..m] | not IsPrime(i)]; [q: n in [2..#NonPrime-1] | IsPrime(q) where q is NonPrime[n-1]+NonPrime[n+1]];

Mathematica

Module[{nps=With[{nn=2000},Complement[Range[nn],Prime[Range[PrimePi[ nn]]]]]},Select[ #[[1]]+#[[3]]&/@Partition[nps,3,1],PrimeQ]] (* Harvey P. Dale, Dec 12 2021 *)

Extensions

Edited by Wolfdieter Lang, Apr 11 2014