A261518 - OEIS

%I #31 Mar 19 2024 03:17:10

%S 1,1,2,6,22,92,508,3674,34452,408104,5925564,103023888,2102941162,

%T 49588317960,1332831700026,40376512041704,1365483356241318,

%U 51130344360226830,2104788801045148866,94659739599219674872,4625501078986781603540,244380566194237434434094

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

%H Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A261518.py">Python program</a>.

%t FoldList[(Prime[#2+#1]-Prime[#2])&,1,Range@15] (* _Ivan N. Ianakiev_, Aug 23 2015 *)

%t RecurrenceTable[{a[n+1] == Prime[n+a[n]] - Prime[n], a[1]==1}, a, {n, 1,16}] (* _G. C. Greubel_, Aug 24 2015 *)

%t nxt[{n_,a_}]:={n+1,Prime[n+a]-Prime[n]}; NestList[nxt,{1,1},16][[All,2]] (* _Harvey P. Dale_, May 15 2018 *)

%o (Haskell)

%o a261518 n = a261518_list !! (n - 1)

%o a261518_list = 1 : zipWith (-)

%o                (map a000040 (zipWith (+) a261518_list [1..])) a000040_list

%o (Magma) [1] cat [n le 1 select 1 else  NthPrime(n + Self(n-1)) - NthPrime(n): n in [1..12]]; // _Vincenzo Librandi_, Aug 24 2015

%o (PARI) a(n) = if(n==1, 1, prime(n-1 + a(n-1)) - prime(n-1));

%o vector(12, n, a(n)) \\ _Altug Alkan_, Oct 05 2015

%o (Python) # see LINKS

%Y Cf. A000040, A001223, A031131, A031165, A031166, A031167, A031168, A031169, A031170, A031171, A031172.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Aug 23 2015

%E a(13)-a(16) from _Ivan N. Ianakiev_, Aug 23 2015

%E a(17)-a(19) from _Jinyuan Wang_, Jun 27 2020

%E a(20)-a(22) from _Lucas A. Brown_, Mar 18 2024