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A191623 Primes of the form 1 + Prod{k=1..n} prime(k)^(2^(k-1)). 1
3, 19, 11251, 2980024297506569894680811251 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes of the form 1 + A191554(k), associated with positions k=1, 2, 3, and 5 there. The next one (if it exists) occurs at k>=15 and has >53500 digits. [Edited by R. J. Mathar, Jun 17 2011 and Joerg Arndt, Jun 21 2011]

This connects A191554 and A191555, which are deeply about primes and monic polynomial irreducible by Eisenstein's Criterion, to primes by another way, connecting additive and multiplicative number theory analogously to the relationship in Primorial primes: A014545, n such that n-th Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime.

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

a(1) = 1 + 2^1 = 1 + 2 = 3 is prime.

a(2) = 1 + (2^1 * 3^2) = 1 + 18 = 19 is prime.

a(3) = 1 + (2^1 * 3^2 * 5^4) = 1 + 11250 = 11251 is prime.

CROSSREFS

Cf. A000040, A191554.

Sequence in context: A098796 A120563 A182344 * A164063 A092828 A117844

Adjacent sequences:  A191620 A191621 A191622 * A191624 A191625 A191626

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Jun 09 2011

STATUS

approved

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Last modified July 21 17:19 EDT 2019. Contains 325198 sequences. (Running on oeis4.)