A274506 Primes one less than the sum over a pair of prime numbers that differ by 8.
13, 17, 29, 53, 113, 149, 269, 353, 389, 809, 1193, 1373, 1409, 1493, 1973, 2069, 2129, 2333, 2393, 2753, 2909, 2969, 3209, 4013, 4493, 4673, 5333, 5693, 6029, 6089, 6449, 6653, 7253, 7529, 7829, 7853, 8429, 8513, 9173, 9293, 10889, 10949, 11393, 11489, 11633, 12413, 12713, 12953, 13049, 13313, 14249, 14969
Offset: 1
Keywords
Examples
13 = 3 + 11 - 1. Note that, (13-7)/2 = 3 and (13+9)/2 = 11 and the prime pairs 3 and 11 differ by 8. 17 = 5 + 13 - 1. Note that, (17-7)/2 = 5 and (17+9)/2 = 13 and the prime pairs 5 and 13 differ by 8.
Programs
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Mathematica
Select[2 Select[Prime@ Range@ 1100, PrimeQ[# + 8] &] + 7, PrimeQ] (* Michael De Vlieger, Jun 26 2016 *)
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PARI
lista(nn) = forprime(p=3, nn, if (isprime((p-7)/2) && isprime((p+9)/2), print1(p, ", "));); \\ Michel Marcus, Jun 25 2016
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Perl
use ntheory ":all"; say for grep{is_prime($)} map { $+$+8-1 } sieve_prime_cluster(1,5e7,8); # _Dana Jacobsen, Apr 27 2017
Comments