A167170 a(6) = 14, for n >= 7, a(n) = a(n-1) + gcd(n, a(n-1)).

14, 21, 22, 23, 24, 25, 26, 39, 40, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 177, 180, 181, 182, 189, 190, 195

Offset: 6

Author

Vladimir Shevelev, Oct 29 2009, Nov 06 2009

Keywords

• nonn

Comments

For every n >= 7, a(n) - a(n-1) is 1 or prime. This Rowland-like "generator of primes" is different from A106108 (see comment to A167168).

Links

• G. C. Greubel, Table of n, a(n) for n = 6..1000
• Eric S. Rowland, A natural prime-generating recurrence, J. of Integer Sequences 11 (2008), Article 08.2.8.
• V. Shevelev, An infinite set of generators of primes based on the Rowland idea and conjectures concerning twin primes, arXiv:0910.4676 [math.NT], 2009.

Crossrefs

Cf. A167168, A106108, A132199, A167054, A167053, A166944, A166945, A116533, A163961, A163963, A084662, A084663, A134162, A135506, A135508, A118679, A120293.

Programs

Maple

A167170 := proc(n) option remember; if n = 6 then 14; else procname(n-1)+igcd(n,procname(n-1)) ; end if; end proc: seq(A167170(i),i=6..80) ; # R. J. Mathar, Oct 30 2010

Mathematica

RecurrenceTable[{a[n] == a[n - 1] + GCD[n, a[n - 1]], a[6] == 14}, a, {n, 6, 100}] (* G. C. Greubel, Jun 04 2016 *)
nxt[{n_,a_}]:={n+1,a+GCD[a,n+1]}; NestList[nxt,{6,14},60][[All,2]] (* Harvey P. Dale, Nov 03 2019 *)

PARI

first(n)=my(v=vector(n-5)); v[1]=14; for(k=7,n, v[k-5]=v[k-6]+gcd(k,v[k-6])); v \\ Charles R Greathouse IV, Aug 22 2017

Extensions

Terms > 91 from R. J. Mathar, Oct 30 2010