A055498 a(0)=0, a(1)=1, a(n) = smallest prime >= a(n-1) + a(n-2).

0, 1, 2, 3, 5, 11, 17, 29, 47, 79, 127, 211, 347, 563, 911, 1481, 2393, 3877, 6271, 10151, 16427, 26591, 43019, 69623, 112643, 182279, 294923, 477209, 772139, 1249361, 2021501, 3270863, 5292367, 8563237, 13855607, 22418849, 36274471, 58693331, 94967809, 153661163

Offset

0,3

Links

Zak Seidov and Robert G. Wilson v, Table of n, a(n) for n = 0..1001 (first 101 terms from Zak Seidov)

Formula

a(n+1) = nextprime(a(n) + a(n-1)) where nextprime(n) is smallest prime >= n.

a(n) is asymptotic to c*phi^n where phi = (1 + sqrt(5))/2 and c = 1.086541275044988562375... - Benoit Cloitre, May 02 2004

a(n) = A055499(n-1) for n>3. - Robert G. Wilson v, Mar 13 2013

a(n) = A007918(a(n-1) + a(n-2)) for n > 1. - Reinhard Zumkeller, Nov 13 2014

Example

After 3, 5, the next prime >=8 is 11.

Mathematica

a[0] = 0; a[1] = 1; a[n_] := a[n] = NextPrime[a[n - 1] + a[n - 2] -1]; Array[a, 37, 0] (* Robert G. Wilson v, Mar 13 2013 *)
RecurrenceTable[{a[0]==0, a[1]==1, a[n]==NextPrime[a[n-1]+a[n-2]-1]}, a, {n, 50}] (* Harvey P. Dale, May 08 2013 *)

Prog

(PARI) a(n)=local(v); if(n<2, n>=0, n++; v=vector(n, i, 1); for(i=3, n, v[i]=nextprime(v[i-1]+v[i-2])); v[n]) /* Michael Somos, Feb 01 2004 */
(Haskell)
a055498 n = a055498_list !! n
a055498_list = 0 : 1 : map a007918
    (zipWith (+) a055498_list $ tail a055498_list)
-- Reinhard Zumkeller, Nov 13 2014

Crossrefs

Cf. A073021, A073022, A055499, A055500, A055501, A055502.

Cf. A007918.

Sequence in context: A084571 A345471 A073021 * A258185 A175247 A298598

Adjacent sequences: A055495 A055496 A055497 * A055499 A055500 A055501

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2000

Status

approved