A072525 - OEIS

%I #13 Jul 21 2017 03:33:02

%S 1,4,9,10,21,22,25,28,33,34,39,40,49,52,55,58,69,70,81,82,85,88,91,

%T 100,111,112,115,118,121,130,133,136,141,142,165,166,171,176,177,182,

%U 185,188,195,202,207,212,219,220,237,242,245,246,253,256,265,276,287,290

%N a(0) = 1; a(n+1) is smallest composite number > a(n) such that a(n) + a(n+1) is prime.

%C The value of a(0) is of minor importance; starting with a(0) = 2, 3, 4, 5, ... results in sequences that differ from this sequence only in a few initial terms.

%C 22, 25, 28 are three and 49,52,55,58 are four consecutive terms in arithmetic progression. Are there k consecutive terms in arithmetic progression for every k?

%e 34 is the next term after 33 since 34 is composite and 33 + 34 = 67 is prime.

%t a=4;lst={a};Do[b=a+1;While[ !PrimeQ[a+b]&&PrimeQ[b],b++ ];AppendTo[lst,b];a=b,{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 07 2010 *)

%o (PARI) {print1(a=1,","); while(a<290,b=a+1; while(isprime(b)||!isprime(a+b),b++); print1(b,","); a=b)}

%Y Cf. A051884, A075570, A262159.

%K nonn

%O 0,2

%A _Amarnath Murthy_, Jul 31 2002

%E Edited and extended by _Klaus Brockhaus_, Aug 01 2002