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*pn-p) then return p fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Jul 31 2020
MATHEMATICA
a[n_] := Module[{p, q = Prime[n]}, For[p = 2, True, p = NextPrime[p], If[PrimeQ[2q-p], Return[p]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 07 2023 *)
PROG
(PARI) {for(n=1, 98, k=2*prime(n); p=2; while(!isprime(k-p), p=nextprime(p+1)); print1(p, ", "))} \\ Klaus Brockhaus, Dec 23 2006
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Mar 23 2004
EXTENSIONS
Edited and extended by Klaus Brockhaus, Dec 23 2006
STATUS
approved