A261518 a(n+1) = prime(n + a(n)) - prime(n), a(1) = 1.

1, 1, 2, 6, 22, 92, 508, 3674, 34452, 408104, 5925564, 103023888, 2102941162, 49588317960, 1332831700026, 40376512041704, 1365483356241318, 51130344360226830, 2104788801045148866, 94659739599219674872, 4625501078986781603540, 244380566194237434434094

Offset: 1

Author

Reinhard Zumkeller, Aug 23 2015

Keywords

• nonn

Links

• Lucas A. Brown, Python program.

Crossrefs

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

Programs

Haskell

a261518 n = a261518_list !! (n - 1)
a261518_list = 1 : zipWith (-)
               (map a000040 (zipWith (+) a261518_list [1..])) a000040_list

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

Mathematica

FoldList[(Prime[#2+#1]-Prime[#2])&,1,Range@15] (* Ivan N. Ianakiev, Aug 23 2015 *)
RecurrenceTable[{a[n+1] == Prime[n+a[n]] - Prime[n], a[1]==1}, a, {n, 1,16}] (* G. C. Greubel, Aug 24 2015 *)
nxt[{n_,a_}]:={n+1,Prime[n+a]-Prime[n]}; NestList[nxt,{1,1},16][[All,2]] (* Harvey P. Dale, May 15 2018 *)

PARI

a(n) = if(n==1, 1, prime(n-1 + a(n-1)) - prime(n-1));
vector(12, n, a(n)) \\ Altug Alkan, Oct 05 2015

Python

# see LINKS

Extensions

a(13)-a(16) from Ivan N. Ianakiev, Aug 23 2015

a(17)-a(19) from Jinyuan Wang, Jun 27 2020

a(20)-a(22) from Lucas A. Brown, Mar 18 2024