login
Primes p such that p + 1024 is also prime.
5

%I #22 Mar 20 2023 18:56:50

%S 7,37,67,73,79,127,139,157,163,193,199,277,283,337,349,409,457,463,

%T 487,499,547,577,613,643,673,709,787,823,853,877,883,907,1039,1063,

%U 1087,1117,1129,1213,1249,1327,1399,1423,1453,1567,1597,1609,1663,1669,1753,1777,1873,1879

%N Primes p such that p + 1024 is also prime.

%C All terms are == 1 (mod 6).

%H Winston de Greef, <a href="/A361485/b361485.txt">Table of n, a(n) for n = 1..10000</a>

%e 139 and 139 + 1024 = 1163 are both prime.

%o (PARI)

%o lista(nn)=my(v=vector(nn), p=2); for(n=1, nn, until(isprime(p+1024), p=nextprime(p+1)); v[n]=p); v \\ _Winston de Greef_, Mar 20 2023

%Y Cf. A000040.

%Y Cf. sequences of the type p + k are primes: A001359 (k = 2), A023200 (k = 4), A023202 (k = 8), A049488 (k = 16), A049489 (k = 32), A049490 (k = 64), A049491 (k = 128), A361483 (k = 256), A361484 (k = 512), this sequence (k = 1024).

%K nonn,easy

%O 1,1

%A _Elmo R. Oliveira_, Mar 13 2023