A163961 - OEIS

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A163961

First differences of A116533.

1, 2, -1, 3, -1, 5, -1, -1, -1, 7, -1, 13, -1, -1, -1, 23, -1, -1, -1, 43, -1, -1, -1, 83, -1, -1, -1, 163, -1, -1, -1, -1, -1, -1, -1, -1, -1, 317, -1, -1, -1, 631, -1, -1, -1, 1259, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2503, -1, -1, -1, 5003, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Ignoring the +-1 terms, we obtain the sequence of Bertrand's primes A006992. If we consider sequences A_i={a_i(n)}, i=1,2,... with the same constructions as A116533, but with initials a_1(1)=2, a_2(1)=11, a_3(1)=17,..., a_m(1)=A164368(m),..., then the union of A_1,A_2,... contains all primes.

LINKS

Table of n, a(n) for n=1..80.

MAPLE

A116533 := proc(n) option remember; if n <=2 then n; else if isprime(procname(n-1)) then 2*procname(n-1) ; else procname(n-1)-1 ; end if; end if; end proc:

A163961 := proc(n) A116533(n+1)-A116533(n) ; end proc: # R. J. Mathar, Sep 03 2011

MATHEMATICA

Differences@ Prepend[NestList[If[PrimeQ@ #, 2 #, # - 1] &, 2, 90], 1] (* Michael De Vlieger, Dec 06 2018 *)

PROG

(PARI) a116533(n) = if(n==1, 1, if(n==2, 2, if(ispseudoprime(a116533(n-1)), 2*a116533(n-1), a116533(n-1)-1)))

a(n) = a116533(n+1)-a116533(n) \\ Felix Fröhlich, Dec 06 2018

(PARI) lista(nn) = {va = vector(nn); va[1] = 1; va[2] = 2; for (n=3, 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 07 2018

CROSSREFS

Cf. A116533, A006992, A055496, A080359, A104272, A106108, A132199, A164368

Sequence in context: A069230 A349348 A242180 * A354366 A101387 A117365

Adjacent sequences: A163958 A163959 A163960 * A163962 A163963 A163964

KEYWORD

sign

AUTHOR

Vladimir Shevelev, Aug 07 2009, Aug 14 2009

STATUS

approved