A255609 a(1)=2; a(n) = the smallest prime p such that a(n)-a(n-1) is semiprime (A001358).

2, 11, 17, 23, 29, 43, 47, 53, 59, 73, 79, 83, 89, 103, 107, 113, 127, 131, 137, 151, 157, 163, 167, 173, 179, 193, 197, 211, 233, 239, 277, 281, 307, 311, 317, 331, 337, 347, 353, 359, 373, 379, 383, 389, 463, 467, 541, 547, 557, 563, 569, 607

Offset: 1

Author

Zak Seidov, Feb 28 2015

Keywords

• nonn

Comments

Sequence with any initial prime term a(1) eventually merges with this sequence: 3,7,11; 5,11; 13,17; 19,23; 31,37,41,47.

For n > 1, a(n) = A289750(n+1). - Jon E. Schoenfield, Nov 26 2017

Examples

			a(2) - a(1) = 11 - 2 = 9 = 3*3;
a(3) - a(2) = 17 - 11 = 6 = 2*3;
a(81) - a(80) = 1009 - 887 = 122 = 2*61.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A156829, A289750.

Programs

Maple

A:= Vector(100): A[1]:= 2:
for n from 2 to 100 do
  p:= A[n-1];
  do
    p:= nextprime(p);
    until numtheory:-bigomega(p-A[n-1]) = 2;
  A[n]:= p;
od:
convert(A,list); # Robert Israel, Dec 28 2022

Mathematica

s = {2}; p = 2; Do[q = NextPrime[p]; While[2 != PrimeOmega[q - p], q = NextPrime[q]]; AppendTo[s, q]; p = q, {100}]; s
sp[n_]:=Module[{p=NextPrime[n]},While[PrimeOmega[p-n]!=2,p= NextPrime[ p]];p]; NestList[sp,2,60] (* Harvey P. Dale, Oct 10 2015 *)

PARI

v=[2];forprime(p=3,300,if(bigomega(p-v[#v])==2,v=concat(v,p)));v \\ Derek Orr, Feb 28 2015