A118134 Primes p such that 4p is the sum of two consecutive primes.

2, 3, 13, 17, 43, 67, 127, 137, 167, 193, 223, 283, 487, 563, 613, 617, 643, 647, 773, 1033, 1187, 1193, 1277, 1427, 1453, 1483, 1543, 1663, 1847, 1949, 2027, 2143, 2297, 2371, 2423, 2437, 2477, 2503, 2609, 2683, 2843, 2857, 2927, 3119, 3137, 3163, 3253, 3433

Offset: 1

Author

Anton Vrba (antonvrba(AT)yahoo.com), May 13 2006

Keywords

• nonn

Comments

From Zak Seidov, Jun 18 2016: (Start)

Minimal difference between odd terms is 4.

a(n+1) - a(n) = 4 for n = {3, 15, 17, 147, 209, 277, 414, 422, 495, 825, 1053, 1380, 1504, 2078, 2264, 2375, 2605, 4224, 4495, 5180, 5825, 6497, 7107, 7372, 8951} and a(n) = {13, 613, 643, 16183, 24763, 37993, 63853, 65323, 81703, 154153, 210853, 295873, 327823, 479023, 537583, 568903, 632323, 1111723, 1195543, 1415833, 1626433, 1853443, 2060503, 2146813, 2702893} == 13 mod 30. (End)

Examples

			13 is there because it is prime and 4*13 = 23+29.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001043 (sums of two consecutive primes).

Programs

Mathematica

pr = Prime[Range[1000]]; Select[(Total /@ Partition[pr, 2, 1])/4, PrimeQ] (* Zak Seidov, Jun 29 2017 *)

PARI

is(n)=isprime(n) && precprime(2*n)+nextprime(2*n)==4*n \\ Charles R Greathouse IV, Apr 24 2015

Extensions

Edited by Don Reble, Jul 23 2006