OFFSET
1,2
COMMENTS
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.
a(18) and a(19) generate 96042- and 192083-decimal digit probable primes. - Serge Batalov, May 27 2024
a(20) generates a 384166-decimal digit probable prime. - Serge Batalov, May 27 2024
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
KEYWORD
nonn,hard,more
AUTHOR
Jeppe Stig Nielsen, May 12 2017
EXTENSIONS
a(14)-a(17) from Serge Batalov, May 26 2024
a(18)-a(20) from Serge Batalov, May 27 2024
STATUS
approved