A286682 a(n) = A059784(n+1) - A059784(n)^2

1, 4, 12, 4, 22, 12, 114, 4, 138, 142, 2956, 6388, 5248

Offset

1,2

Comments

This sequence relates to A059784 just like A108739 relates to the Mills primes A051254.

That this leads to a Mills-like real constant C such that floor(C^2^n) is a prime number for any natural number n, requires a proof of Legendre's conjecture that there is always a prime between consecutive perfect squares.

Links

Table of n, a(n) for n=1..13.

Example

A059784(8) by construction can be written ((((((2^2 + 1)^2 + 4)^2 + 12)^2 + 4)^2 + 22)^2 + 12)^2 + 114. Taking out the addends gives 1, 4, 12, 4, 22, 12, 114 which lists the first seven terms of this sequence.

Mathematica

Map[#2 - #1^2 & @@ # &, Partition[NestList[NextPrime[#^2] &, 2, 12], 2, 1]] (* Michael De Vlieger, May 12 2017 *)

Prog

(PARI) p=2; while(1, a=nextprime(p^2); print1(a-p^2, ", "); p=a)

Crossrefs

Cf. A059784, A108739, A051254.

Sequence in context: A224512 A010296 A084351 * A262621 A255289 A348334

Adjacent sequences: A286679 A286680 A286681 * A286683 A286684 A286685

Keyword

more,hard,nonn

Author

Jeppe Stig Nielsen, May 12 2017

Status

approved