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A193298
Gica-Panaitopol recursion: a(1) = 1; a(n+1) = 2*a(n) if a(n) <= n; otherwise a(n+1) = a(n) - 1.
5
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.
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
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Jul 21 2011
STATUS
approved