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%I #10 Jul 31 2015 21:45:43
%S 3,13,61,71,83,167,197,241,271,281,283,317,347,349,379,431,457,499,
%T 503,569,617,631,641,643,701,757,761,797,827,829,863,1061,1151,1163,
%U 1217,1321,1381,1471,1481,1483,1531,1543,1553,1609,1619,1667,1669,1777,1877
%N Primes such that the sum of the predecessor and successor primes is divisible by 7.
%H Harvey P. Dale, <a href="/A112731/b112731.txt">Table of n, a(n) for n = 1..1000</a>
%e a(1) = 3 because previousprime(3) + nextprime(3) = 2 + 5 = 7.
%e a(2) = 13 because previousprime(13) + nextprime(13) = 11 + 17 = 28 = 7 * 4.
%e a(3) = 61 because previousprime(61) + nextprime(61) = 59 + 67 = 126 = 7 * 18.
%e a(4) = 71 because previousprime(71) + nextprime(71) = 67 + 73 = 140 = 7 * 20.
%t For[n = 2, n < 300, n++, If[(Prime[n - 1] + Prime[n + 1])/7 == Floor[(Prime[n - 1] + Prime[n + 1])/7], Print[Prime[n]]]] (* _Stefan Steinerberger_ *)
%t Prime@Select[Range[2, 298], Mod[Prime[ # - 1] + Prime[ # + 1], 7] == 0 &] (* _Robert G. Wilson v_, Jan 11 2006 *)
%t Transpose[Select[Partition[Prime[Range[7000]],3,1],Divisible[First[#]+ Last[#],7]&]][[2]] (* _Harvey P. Dale_, Jun 11 2013 *)
%Y Cf. A000040, A112681, A112794, A112731, A112789, A112795, A112796, A112804, A112847, A112859, A113155, A113156, A113157, A113158.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Dec 31 2005
%E More terms from _Stefan Steinerberger_ and _Robert G. Wilson v_, Jan 02 2006
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