A193298 Gica-Panaitopol recursion: a(1) = 1; a(n+1) = 2*a(n) if a(n) <= n; otherwise a(n+1) = a(n) - 1.

1, 2, 4, 3, 6, 5, 10, 9, 8, 16, 15, 14, 13, 26, 25, 24, 23, 22, 21, 20, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69

Offset

1,2

Comments

Using the Prime Number Theorem, Gica and Panaitopol show that the sequence contains infinitely many primes.

References

A. Gica and L. Panaitopol, An application of the prime element theorem, Gazeta Matematica 21(100), No. 2 (2003), 113-115.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

The terms occur in disjoint blocks of decreasing consecutive numbers: 1; 2; 4, 3; 6, 5; 10, 9, 8; 16, 15, 14, 13; 26, 25, 24, 23, 22, 21, 20; . . .

Mathematica

a[1] = 1; a[n_] := a[n] = If[a[n-1] <= n-1, 2*a[n-1], a[n-1]-1]; Table[a[n], {n, 100}]

Crossrefs

Cf. A193299 (sorted sequence), A193300 (subset of primes), A193301 (complement of sorted sequence).

Sequence in context: A132666 A116533 A087559 * A168007 A359114 A328108

Adjacent sequences: A193295 A193296 A193297 * A193299 A193300 A193301

Keyword

nonn

Author

Jonathan Sondow, Jul 21 2011

Status

approved