

A304903


Least prime p such that 2*n^2  p is prime.


3



3, 5, 3, 3, 5, 19, 19, 5, 3, 3, 5, 7, 3, 7, 3, 7, 5, 3, 3, 5, 31, 7, 23, 13, 31, 5, 19, 13, 11, 43, 19, 17, 3, 3, 13, 7, 31, 5, 13, 3, 11, 7, 19, 23, 3, 61, 5, 3, 7, 5, 61, 37, 5, 3, 3, 7, 19, 3, 7, 31, 7, 5, 13, 3, 5
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OFFSET

2,1


COMMENTS

Each square > 1 can be written as the average of 2 primes p1 < p2. a(n) gives the least prime p1 such that n^2 = (p1 + p2) / 2. The corresponding p2 is provided in A304904.


LINKS



FORMULA



EXAMPLE

a(5) = 3 because 2*5^2  3 = 47 is prime,
a(7) = 19 because 2*7^2  19 = 71 is prime, whereas all of 98  3 = 95, 98  5 = 93, 98  7 = 91, 98  11 = 87, 98  13 = 85 and 98  17 = 81 are composite.


MATHEMATICA

f[n_] := Block[{p = 2}, While[ !PrimeQ[2 n^2  p], p = NextPrime@ p]; p]; Array[f, 65, 2] (* Robert G. Wilson v, May 20 2018 *)


PROG

(PARI) a(n) = forprime(p=3, , if(ispseudoprime(2*n^2p), return(p))) \\ Felix Fröhlich, May 20 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



