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%I #13 May 03 2017 07:54:14
%S 149,433,463,491,839,907,929,953,1217,1451,1741,2789,2957,3853,3917,
%T 4493,4639,4957,5021,5167,5227,5569,6353,6673,6733,6823,7219,7481,
%U 7573,7649,7919,8293,8443,8699,9281,9421,9743,9923,10151,10211,10709,11161
%N Primes such that the sum of the predecessor and successor primes is divisible by 29.
%C There is a trivial analogy to every prime beyond 3, but mod 2. A112681 is analogous to this, but mod 3. A112731 is analogous to this, but mod 7. A112789 is analogous to this, but mod 11.
%H Robert Israel, <a href="/A112859/b112859.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = prime(i) is in this sequence iff prime(i-1)+prime(i+1) = 0 mod 29. a(n) = A000040(i) is in this sequence iff A000040(i-1)+A000040(i+1) = 0 mod 29.
%e a(1) = 149 because prevprime(149) + nextprime(149) = 139 + 151 = 290 = 29 * 10.
%e a(2) = 433 because prevprime(433) + nextprime(433) = 431 + 439 = 870 = 29 * 30.
%e a(3) = 463 because prevprime(463) + nextprime(463) = 461 + 467 = 928 = 29 * 32.
%e a(4) = 491 because prevprime(491) + nextprime(491) = 487 + 499 = 986 = 29 * 34.
%p Primes:= select(isprime, [seq(i,i=3..20000,2)]):
%p R:= select(t -> Primes[t-1]+Primes[t+1] mod 29 = 0, [$2..nops(Primes)-1]):
%p Primes[R]; # _Robert Israel_, May 02 2017
%t Prime@ Select[Range[2, 1372], Mod[Prime[ # - 1] + Prime[ # + 1], 29] == 0 &] (* _Robert G. Wilson v_, Jan 05 2006 *)
%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_, Jan 01 2006
%E More terms from _Robert G. Wilson v_, Jan 05 2006
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