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

1,1

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

Links

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A001358, A156829, A289750.

Sequence in context: A253474 A133410 A156829 * A105840 A243960 A336368

Adjacent sequences: A255606 A255607 A255608 * A255610 A255611 A255612

Keyword

nonn

Author

Zak Seidov, Feb 28 2015

Status

approved