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

1,1

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

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)<m-2*n) and isprime (m-2*n)) do od; b(n):= m-2*n; m fi end: seq (a(n), n=1..100);  # Alois P. Heinz, Feb 05 2009

Crossrefs

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

Sequence in context: A068072 A136292 A088046 * A087373 A155030 A030468

Adjacent sequences: A155879 A155880 A155881 * A155883 A155884 A155885

Keyword

base,easy,nonn

Author

Eric Angelini, Jan 29 2009

Extensions

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

Status

approved