A163963 First differences of A080735.

1, 2, 1, 5, 1, 11, 1, 23, 1, 47, 1, 1, 1, 97, 1, 1, 1, 197, 1, 1, 1, 397, 1, 1, 1, 797, 1, 1, 1, 1597, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3203, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6421, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12853, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 25717, 1, 1, 1, 51437, 1, 1, 1

Offset

1,2

Comments

Ignoring the 1 terms we obtain A055496. If we consider sequences A_i={a_i(n)}, i=1,2,... with the same constructions as A080735, but with initials a_1(1)=2, a_2(1)=3, a_3(1)=13,..., a_m(1)=A080359(m),..., then the union of A_1,A_2,... contains all primes.

Links

G. C. Greubel, Table of n, a(n) for n = 1..5000

Maple

A080735 := proc(n) option remember; local p ; if n = 1 then 1; else p := procname(n-1) ; if isprime(p) then 2*p; else p+1 ; end if; end if; end proc: A163963 := proc(n) A080735(n+1)-A080735(n) ; end: seq(A163963(n), n=1..100) ; # R. J. Mathar, Nov 05 2009

Mathematica

Differences@ NestList[If[PrimeQ@ #, 2 #, # + 1] &, 1, 87] (* Michael De Vlieger, Dec 06 2018, after Harvey P. Dale at A080735 *)

Prog

(PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = if (isprime(va[n-1]), 2*va[n-1], va[n-1]+1); ); vector(nn-1, n, va[n+1] - va[n]); } \\ Michel Marcus, Dec 06 2018

Crossrefs

Cf. A116533, A163961, A080735, A006992, A055496, A080359, A104272, A106108, A132199.

Sequence in context: A115123 A132081 A054251 * A119763 A363087 A092142

Adjacent sequences: A163960 A163961 A163962 * A163964 A163965 A163966

Keyword

nonn

Author

Vladimir Shevelev, Aug 07 2009

Extensions

More terms from R. J. Mathar, Nov 05 2009

Status

approved