A166945 Records of first differences of A166944.

2, 3, 7, 13, 43, 139, 313, 661, 1321, 2659, 5419, 10891, 22039, 44383, 88801, 177841, 355723, 713833, 1427749, 2860771, 5725453, 11461141, 22933441, 45895573, 91793059, 183616423, 367232911, 734482123, 1468965061, 2937930211, 5875882249, 11751795061, 23503590559, 47007181621, 94014363763

Offset

1,1

Comments

Conjecture. Each term of the sequence is the greater of a pair of twin primes (A006512).

Links

Table of n, a(n) for n=1..35.

E. S. Rowland, A natural prime-generating recurrence, Journal of Integer Sequences, Vol.11(2008), Article 08.2.8. arXiv:0710.3217 [math.NT]

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.

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

Mathematica

Reap[Print[old = r = 2]; Sow[old]; For[n = 2, n <= 10^6, n++, d = GCD[old, If[OddQ[n], n-2, n]]; If[d>r, r=d; Print[d]; Sow[d]]; old += d]][[2, 1]] (* Jean-François Alcover, Nov 03 2018, from PARI *)

Prog

(PARI) print1(old=r=2); for(n=2, 1e11, d=gcd(old, if(n%2, n-2, n)); if(d>r, r=d; print1(", "d)); old+=d) \\ Charles R Greathouse IV, Oct 13 2017

Crossrefs

Cf. A166944, A084662, A084663, A106108, A132199, A134162, A135506, A135508, A118679, A120293.

Sequence in context: A007996 A206579 A349327 * A257393 A273814 A371131

Adjacent sequences: A166942 A166943 A166944 * A166946 A166947 A166948

Keyword

nonn

Author

Vladimir Shevelev, Oct 24 2009, Nov 05 2009

Extensions

6 more terms from R. J. Mathar, Nov 19 2009; extension beginning with a(19) from Benoit Cloitre (private communication to Vladimir Shevelev)

a(25), a(26) from D. S. McNeil, Dec 13 2010

a(27)-a(30) from Charles R Greathouse IV, Oct 13 2017

a(31)-a(35) from Charles R Greathouse IV, Oct 17 2017

Status

approved