

A092938


a(n) = least prime p such that 2*prime(n)  p is prime.


3



2, 3, 3, 3, 3, 3, 3, 7, 3, 5, 3, 3, 3, 3, 5, 3, 5, 13, 3, 3, 7, 7, 3, 5, 3, 3, 7, 3, 7, 3, 3, 5, 3, 7, 5, 19, 3, 13, 3, 29, 5, 3, 3, 3, 5, 19, 3, 3, 5, 19, 3, 11, 3, 3, 5, 3, 17, 19, 7, 5, 3, 17, 7, 3, 7, 3, 3, 13, 3, 7, 5, 17, 7, 3, 7, 5, 5, 7, 5, 7, 11, 3, 3, 3, 19, 3, 11, 3, 3, 7, 5, 5, 3, 5, 7, 23, 5, 3
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OFFSET

1,1


COMMENTS

a(n) = least prime p such that prime(n) = (p+q)/2, where q is also prime.
a(n) <= prime(n). Conjecture: a(n) = prime(n) only for n = 1 and 2.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

2*prime(8) = 38; 38  2 = 36, 38  3 = 35, 38  5 = 33 are composite, but 38  7 = 31 is prime. Hence a(8) = 7.


MAPLE

f:= proc(n) local pn, p;
pn:= ithprime(n);
p:= 1;
do
p:= nextprime(p);
if isprime(2*pnp) then return p fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 31 2020


PROG

(PARI) {for(n=1, 98, k=2*prime(n); p=2; while(!isprime(kp), p=nextprime(p+1)); print1(p, ", "))} \\ Klaus Brockhaus, Dec 23 2006


CROSSREFS

Cf. A092939, A092940, A116619.
Sequence in context: A035441 A025784 A035390 * A320110 A068953 A189635
Adjacent sequences: A092935 A092936 A092937 * A092939 A092940 A092941


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Mar 23 2004


EXTENSIONS

Edited and extended by Klaus Brockhaus, Dec 23 2006


STATUS

approved



