A155882 Smallest positive prime number such that a(n)-2n is also prime, a(n) < a(n+1), and the differences a(n)-2n must increase with n.

5, 11, 17, 31, 41, 53, 61, 83, 89, 103, 131, 137, 157, 167, 179, 199, 227, 233, 271, 281, 293, 307, 317, 331, 367, 383, 401, 409, 431, 439, 463, 503, 509, 547, 557, 563, 577, 599, 619, 643, 653, 661, 673, 701, 709, 733, 821, 829, 859, 887, 911, 967, 983, 991

Offset: 1

Author

Eric Angelini, Jan 29 2009

Keywords

• base
• easy
• nonn

Comments

Subtracting from a(1) twice n=1 gives 5-2=3, which is a prime number; subtracting from a(2) twice n=2 gives 11-4=7, which is a prime number; subtracting from a(3) twice n=3 gives 17-6=11, which is a prime number; subtracting from a(4) twice n=4 gives 31-8=23, which is a prime number; etc.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020484, A108184 (for the differences a(n)-2n).

Programs

Maple

b:= proc(n) option remember; global a; a(n); b(n) end: a:= proc(n) option remember; local m; global b; if n=1 then b(1):= 3; 5 else for m from a(n-1)+2 by 2 while not (isprime(m) and (b(n-1)Alois P. Heinz, Feb 05 2009

Extensions

Corrected definition and more terms from Alois P. Heinz, Feb 05 2009