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

1,1

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)

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A001043 (sums of two consecutive primes).

Sequence in context: A215359 A115898 A215350 * A215386 A352539 A338216

Adjacent sequences: A118131 A118132 A118133 * A118135 A118136 A118137

Keyword

nonn

Author

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

Extensions

Edited by Don Reble, Jul 23 2006

Status

approved