A031172 -id:A031172 - cp's OEIS frontend

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

Reinhard Zumkeller, Aug 23 2015

nonn

Lucas A. Brown, Python program.

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

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

[1] cat [n le 1 select 1 else  NthPrime(n + Self(n-1)) - NthPrime(n): n in [1..12]]; // Vincenzo Librandi, Aug 24 2015

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 *)

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
```

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

A214612 prime(n^3) - prime(n).

Original entry on oeis.org

0, 16, 98, 304, 680, 1308, 2292, 3652, 5496, 7890, 10926, 14716, 19362, 24766, 31272, 38820, 47598, 57498, 68964, 81728, 96064, 112212, 129990, 149628, 171432, 194942, 220758, 248744, 279322, 312470, 347580, 385962, 427032, 470794, 517404, 567720, 620374

Offset: 1

Jonathan Vos Post, Mar 06 2013

This is to exponent 3 as A213926 is to exponent 2.

			a(1) = prime(1^3) - prime(1) = 2-2 = 0.
a(2) = prime(2^3) - prime(2) = 19-3 = 16.
a(3) = prime(3^3) - prime(3) = 103-5 = 98.

Cf. A000040, A001223, A031131, A031165-A031172, A072473, A092504, A213926.

Table[Prime[n^3] - Prime[n], {n, 50}] (* T. D. Noe, Mar 07 2013 *)

cp's OEIS Frontend

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

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