A289750 - OEIS

%I #20 Nov 27 2017 02:33:49

%S 3,7,11,17,23,29,43,47,53,59,73,79,83,89,103,107,113,127,131,137,151,

%T 157,163,167,173,179,193,197,211,233,239,277,281,307,311,317,331,337,

%U 347,353,359,373,379,383,389,463,467,541,547,557,563,569,607,613,617,631,641,647,653,659

%N a(1) = 3 and a(n+1) - a(n) = 2*p where p is the least possible prime.

%C Values of p: 2, 2, 3, 3, 3, 7, 2, 3, 3, 7, 3, 2, 3, 7, 2, 3, 7, 2, 3, 7, 3, 3, 2, 3, 3, 7, 2, 7, 11, 3, 19, 2, 13, 2, 3, 7, 3, 5, 3, 3, 7, 3, 2, 3, 37, 2, 37, 3, 5.

%C For n > 2, a(n) = A255609(n-1). - _Jon E. Schoenfield_, Nov 26 2017

%H Charles R Greathouse IV, <a href="/A289750/b289750.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1000) = 23833 = A000040(2651), a(999) = 23819 = A000040(2649), and a(1000)-a(999) = 14 = 2*A000040(4), while 23819 + {4,6,10} are composite.

%o (PARI) step(n)=forprime(p=2,, if(isprime(n+2*p), return(n+2*p)))

%o first(n)=my(v=vector(n)); v[1]=3; for(n=2,n, v[n]=step(v[n-1])); v \\ _Charles R Greathouse IV_, Jul 14 2017

%Y Cf. A001223, A255609, A289750.

%K nonn,easy

%O 1,1

%A _Zak Seidov_, Jul 11 2017