login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A167493 a(1) = 2; thereafter a(n) = a(n-1) + gcd(n, a(n-1)) if n is odd, and a(n) = a(n-1) + gcd(n-2, a(n-1)) if n is even. 4
2, 4, 5, 6, 7, 8, 9, 12, 15, 16, 17, 18, 19, 20, 25, 26, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 52, 53, 54, 55, 60, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 124, 125, 126 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjectures. 1) For n >= 2, every difference a(n) - a(n-1) is 1 or prime; 2) Every record of differences a(n) - a(n-1) greater than 3 belongs to the sequence of the greater of twin primes (A006512).

LINKS

Table of n, a(n) for n=1..66.

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, Three theorems on twin primes, arXiv:0911.5478 [math.NT], 2009-2010.

MATHEMATICA

nxt[{n_, a_}]:={n+1, If[EvenQ[n], a+GCD[n+1, a], a+GCD[n-1, a]]}; Transpose[ NestList[nxt, {1, 2}, 70]][[2]] (* Harvey P. Dale, Dec 05 2015 *)

PROG

(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 2; for (n=2, nn, va[n] = if (n%2, va[n-1] + gcd(n, va[n-1]), va[n-1] + gcd(n-2, va[n-1])); ); va; } \\ Michel Marcus, Dec 13 2018

CROSSREFS

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

Cf also A006512, A167494.

Sequence in context: A188372 A088384 A026446 * A328107 A039121 A138367

Adjacent sequences:  A167490 A167491 A167492 * A167494 A167495 A167496

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Nov 05 2009

EXTENSIONS

More terms from Harvey P. Dale, Dec 05 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 22 15:05 EST 2020. Contains 332137 sequences. (Running on oeis4.)