A086505 a(n) is the n-th smallest prime p such that p+2n is also prime.

3, 7, 11, 23, 31, 29, 53, 73, 53, 89, 157, 73, 137, 199, 73, 281, 229, 127, 383, 229, 149, 389, 463, 193, 359, 547, 239, 467, 823, 197, 857, 883, 283, 809, 499, 389, 1013, 907, 421, 827, 1201, 373, 1151, 1231, 367, 1307, 1279, 577, 1229, 1009, 631, 1427, 1783

Offset: 1

Author

Amarnath Murthy, Jul 29 2003

Keywords

• nonn

Comments

Note the patterns in the graph. These patterns depend on the number of prime factors of n: see color graph for different n's: n primes - black dots, n multiples of 3 - red dots, n multiples of 15 - green dots, n multiples of 105 - blue dots. - Zak Seidov, Nov 28 2013

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Zak Seidov, Color graph for different n's

Crossrefs

Cf. A020483, A231608.

Programs

Maple

N:= 10^4: # to get all terms before the first with a(n)+2*n > N
Primes:= select(isprime, {seq(2*i+1, i=1..N)}):
for n from 1 do
R:= Primes intersect map(`+`, Primes, -2*n);
if nops(R) < n then break fi;
A[n]:= R[n];
od:
seq(A[j],j=1..n-1); # Robert Israel, Aug 07 2014

Extensions

Edited by Sam Alexander, Feb 26 2004