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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. 1

%I

%S 5,11,17,31,41,53,61,83,89,103,131,137,157,167,179,199,227,233,271,

%T 281,293,307,317,331,367,383,401,409,431,439,463,503,509,547,557,563,

%U 577,599,619,643,653,661,673,701,709,733,821,829,859,887,911,967,983,991

%N 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.

%C 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.

%H Alois P. Heinz, <a href="/A155882/b155882.txt">Table of n, a(n) for n = 1..1000</a>

%p 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

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

%K base,easy,nonn

%O 1,1

%A _Eric Angelini_, Jan 29 2009

%E Corrected definition and more terms from _Alois P. Heinz_, Feb 05 2009

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Last modified April 21 19:16 EDT 2021. Contains 343156 sequences. (Running on oeis4.)