cp's OEIS Frontend

A163963 First differences of A080735.

%I A163963 #14 Dec 06 2018 16:34:38
%S A163963 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,
%T A163963 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,
%U A163963 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
%N A163963 First differences of A080735.
%C A163963 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.
%H A163963 G. C. Greubel, <a href="/A163963/b163963.txt">Table of n, a(n) for n = 1..5000</a>
%p A163963 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
%t A163963 Differences@ NestList[If[PrimeQ@ #, 2 #, # + 1] &, 1, 87] (* _Michael De Vlieger_, Dec 06 2018, after _Harvey P. Dale_ at A080735 *)
%o A163963 (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
%Y A163963 Cf. A116533, A163961, A080735, A006992, A055496, A080359, A104272, A106108, A132199.
%K A163963 nonn
%O A163963 1,2
%A A163963 _Vladimir Shevelev_, Aug 07 2009
%E A163963 More terms from _R. J. Mathar_, Nov 05 2009