%I #30 Mar 22 2018 16:29:00
%S 2,3,13,17,43,67,127,137,167,193,223,283,487,563,613,617,643,647,773,
%T 1033,1187,1193,1277,1427,1453,1483,1543,1663,1847,1949,2027,2143,
%U 2297,2371,2423,2437,2477,2503,2609,2683,2843,2857,2927,3119,3137,3163,3253,3433
%N Primes p such that 4p is the sum of two consecutive primes.
%C From _Zak Seidov_, Jun 18 2016: (Start)
%C Minimal difference between odd terms is 4.
%C 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)
%H Charles R Greathouse IV, <a href="/A118134/b118134.txt">Table of n, a(n) for n = 1..10000</a>
%e 13 is there because it is prime and 4*13 = 23+29.
%t pr = Prime[Range[1000]]; Select[(Total /@ Partition[pr, 2, 1])/4, PrimeQ] (* _Zak Seidov_, Jun 29 2017 *)
%o (PARI) is(n)=isprime(n) && precprime(2*n)+nextprime(2*n)==4*n \\ _Charles R Greathouse IV_, Apr 24 2015
%Y Cf. A001043 (sums of two consecutive primes).
%K nonn
%O 1,1
%A Anton Vrba (antonvrba(AT)yahoo.com), May 13 2006
%E Edited by _Don Reble_, Jul 23 2006
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