A168143 a(17)=37; for n>=17, a(n)=3n-14 if gcd(n,a(n-1))>1 and all prime divisors of n more than 17; a(n)=a(n-1)+1, otherwise.

37, 38, 43, 44, 45, 46, 55, 56, 57, 58, 59, 60, 61, 62, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157

Offset: 17

Author

Vladimir Shevelev, Nov 19 2009

Keywords

• nonn

Comments

a(n+1)-a(n)+14 is either 15 or a prime > 17. For a generalization, see the second Shevelev link. - Edited by Robert Israel, Aug 21 2017

Links

• Robert Israel, Table of n, a(n) for n = 17..10000
• E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol. 11 (2008), Article 08.2.8.
• V. Shevelev, A new generator of primes based on the Rowland idea, arXiv:0910.4676 [math.NT], 2009.
• V. Shevelev, Generalizations of the Rowland theorem, arXiv:0911.3491 [math.NT], 2009-2010.

Crossrefs

Cf. A167495, A167494, A167493, A167197, A167195, A167170, A167168, A106108, A132199, A167054, A167053, A166944, A166945, A116533, A163961, A163963, A084662, A084663, A134162, A135506, A135508, A118679, A120293.

Programs

Maple

A[17]:= 37:
q:= convert(select(isprime,[$2..17]),`*`);
for n from 18 to 100 do
  if igcd(n,A[n-1]) > 1 and igcd(n,q) = 1 then A[n]:= 3*n-14
    else A[n]:= A[n-1]+1 fi
od:
seq(A[i],i=17..100); # Robert Israel, Aug 21 2017

Mathematica

nxt[{n_,a_}]:={n+1,If[GCD[n+1,a]>1&&FactorInteger[n+1][[1,1]]>17,3(n+1)-14,a+1]}; NestList[nxt,{17,37},60][[All,2]] (* Harvey P. Dale, Aug 15 2017 *)

Extensions

Corrected by Harvey P. Dale, Aug 15 2017