A002715 An infinite coprime sequence defined by recursion. (Formerly M2683 N1073)

3, 7, 23, 47, 1103, 2207, 2435423, 4870847, 11862575248703, 23725150497407, 281441383062305809756861823, 562882766124611619513723647, 158418504200047111075388369241884118003210485743490303

Offset

0,1

Comments

Every term is relatively prime to all others.

Every term is congruent to 3 mod 4. - Peter Munn, Apr 08 2026

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..21

A. W. F. Edwards, Infinite coprime sequences, Math. Gaz., 48 (1964), 416-422.

A. W. F. Edwards, Infinite coprime sequences, Math. Gaz., 48 (1964), 416-422. [Annotated scanned copy]

R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018.

Formula

a(2n+1) = 2*a(2n)+1, a(2n) = (a(2n-1)^2-3)/2, with a(0)=3.

Mathematica

a[n_?OddQ] := a[n] = 2*a[n-1] + 1; a[n_?EvenQ] := a[n] = (a[n-1]^2 - 3)/2; a[0] = 3; Table[a[n], {n, 0, 12}] (* Jean-François Alcover, Jan 25 2013 *)

Prog

(PARI) a(n)=if(n<1, 3*(n==0), if(n%2, 2*a(n-1)+1, (a(n-1)^2-3)/2))

Crossrefs

Other infinite coprime sequences with a recursive definition: A000058, A000215, A000289, A001566, A001601, A001685, A002716, A002812, A002814, A003686, A006695, A064526\{0}.

Subsequence of A004767.

Sequence in context: A054270 A058000 A246497 * A112052 A205491 A203253

Adjacent sequences: A002712 A002713 A002714 * A002716 A002717 A002718

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Jeffrey Shallit

Edited by Michael Somos, Feb 01 2004

Status

approved