

A091666


Difference between prime(n)^2 and the next prime.


10



1, 2, 4, 4, 6, 4, 4, 6, 12, 12, 6, 4, 12, 12, 4, 10, 10, 6, 4, 10, 4, 6, 10, 6, 4, 10, 4, 18, 6, 12, 10, 6, 4, 12, 28, 6, 10, 4, 4, 18, 10, 10, 12, 4, 12, 6, 10, 10, 10, 12, 4, 10, 18, 28, 18, 22, 6, 12, 4, 16, 18, 4, 4, 10, 4, 4, 6, 22, 4, 42, 24, 22, 10, 4
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OFFSET

1,2


COMMENTS

Conjecturally, a(n) << log^2 n (with constant around 8/e^gamma in the supremum). [Charles R Greathouse IV, Dec 27 2011]
Except for a(2)=2, there are no terms = 2 mod 6 (as p^2+2 = 0 mod 3 for primes p > 3). Also, only 1 and 2 appear once while all other terms may appear (infinitely) many times. [Zak Seidov, Apr 18 2012]


LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000


EXAMPLE

prime(3)=5, 5*5=25 for k=4 25+4=29 prime, k=4 is the least k with prime(3)^2 + k prime.


MATHEMATICA

NextPrime[#^2]#^2&/@Prime[Range[74]] (* Zak Seidov, Apr 18 2012 *)


CROSSREFS

Cf. A001248, A062772, A054271, A133517, A133518, A133519, A133520, A133521, A133522, A001223.
Sequence in context: A205969 A326771 A049782 * A084290 A062011 A225520
Adjacent sequences: A091663 A091664 A091665 * A091667 A091668 A091669


KEYWORD

easy,nonn


AUTHOR

Pierre CAMI, Jan 27 2004


STATUS

approved



