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

17,1

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.

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 *)

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.

Sequence in context: A346383 A337453 A071887 * A111043 A041683 A064172

Adjacent sequences: A168140 A168141 A168142 * A168144 A168145 A168146

Keyword

nonn,uned

Author

Vladimir Shevelev, Nov 19 2009

Extensions

Corrected by Harvey P. Dale, Aug 15 2017

Status

approved