A249807 a(0) = 1; afterwards a(n) is the smallest positive square that added to all previous terms produces a prime.

1, 1, 1, 4, 4, 36, 36, 144, 36, 324, 324, 36, 36, 36, 144, 144, 144, 36, 36, 36, 900, 900, 900, 324, 900, 36, 324, 36, 324, 576, 324, 144, 36, 324, 36, 576, 144, 2304, 576, 36, 144, 900, 324, 144, 576, 324, 900, 36, 144, 900, 2916, 144, 2916, 36, 576, 900, 1764, 324, 144, 1296, 36, 36

Offset

0,4

Comments

All terms starting with a(5) are multiples of 36.

a(n) exists for all n under the Hardy-Littlewood Conjecture F. - Charles R Greathouse IV, Nov 06 2014

Links

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Example

1+1+1+4=7(prime), 7+4=11(prime), 11+36=47(prime), 47+36=83(prime).

Mathematica

nxt[{t_, a_}]:=Module[{k=1}, While[!PrimeQ[t+k^2], k++]; {t+k^2, k^2}]; NestList[nxt, {1, 1}, 70][[;; , 2]] (* Harvey P. Dale, Jul 28 2023 *)

Prog

(PARI) first(n)=n=max(n, 5); my(v=vector(n+1, i, 1), k, s=11); v[4]=v[5]=4; for(i=6, #v, k=6; while(!isprime(s+k^2), k+=6); s+=v[i]=k^2); v \\ Charles R Greathouse IV, Nov 06 2014

Crossrefs

Cf. A073609.

Sequence in context: A145109 A181858 A227511 * A180064 A105350 A335183

Adjacent sequences: A249804 A249805 A249806 * A249808 A249809 A249810

Keyword

nonn,easy

Author

Zak Seidov, Nov 06 2014

Status

approved