A129726 - OEIS

%I #36 Jan 19 2024 16:56:13

%S 2,5,9,13,19,23,29,33,39,47,51,59,65,69,75,83,91,95,103,109,113,121,

%T 127,135,145,151,155,161,165,171,187,193,201,205,217,221,229,237,243,

%U 251,259,263,275,279,285,289,303,317,323,327

%N a(n) = a(n-1) + prime(n) - prime(n-1) + 2; a(1) = 2.

%C The sequence shows 36 primes in the first 100 entries; the largest run of primes in these has length 4.

%H Vincenzo Librandi, <a href="/A129726/b129726.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = a(n-1) + A001223(n-1) + 2.

%F a(n) = prime(n) + 2*n - 2. - _Bill McEachen_, Dec 02 2023

%p A129726:= proc(n) option remember;

%p     if n = 1 then 2;

%p     else procname(n-1)+2+ithprime(n)-ithprime(n-1);

%p     end if; end proc:

%p seq(A129726(n), n=1..50) ; # _R. J. Mathar_, Feb 01 2014

%t a[n_]:= a[n]= If[n==1, 2, a[n-1] +Prime[n] -Prime[n-1] +2]; Table[a[n], {n,50}]

%t RecurrenceTable[{a[1]==2,a[n]==a[n-1]+2+Prime[n]-Prime[n-1]},a,{n,50}] (* _Harvey P. Dale_, Apr 02 2018 *)

%o (PARI) a(n) = if(n==1, 2, a(n-1) +prime(n) -prime(n-1) +2); \\ _G. C. Greubel_, Dec 02 2019

%o (Magma)

%o function a(n)

%o   if n eq 1 then return 2;

%o   else return a(n-1) + NthPrime(n) - NthPrime(n-1) + 2;

%o   end if; return a; end function;

%o [a(n): n in [1..50]]; // _G. C. Greubel_, Dec 02 2019

%o (Sage)

%o def a(n):

%o     if (n==1): return 2

%o     else: return a(n-1) + nth_prime(n) - nth_prime(n-1) + 2

%o [a(n) for n in (1..50)] # _G. C. Greubel_, Dec 02 2019

%Y Cf. A000040, A001223, A005843.

%K nonn,easy

%O 1,1

%A _Roger L. Bagula_, May 12 2007