

A118134


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


8



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
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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 A143871 A225517
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



