OFFSET
1,1
COMMENTS
Conjecture: for every composite k there is at least one such prime.
LINKS
Robert Israel, Table of n, a(n) for n = 1..1000
EXAMPLE
a(3) = 15 because 15 is composite, the numbers from 1 to 14 coprime to 15 are 1, 2, 4, 7, 8, 11, 13, 14, and the 3 primes 47 = 1+2+4+7+8+11+14, 53 = 1+2+4+8+11+13+14 and 59 = 2+4+7+8+11+13+14 are sums of all but one of these.
MAPLE
f:= proc(n) local C, s;
C:= select(t -> igcd(t, n)=1, [$1..n-1]);
s:= convert(C, `+`);
nops(select(isprime, map(t -> s-t, C)))
end proc:
N:= 100; # for a(1)..a(N)
V:= Vector(N): count:= 0:
for nn from 4 while count < N do
if isprime(nn) then next fi;
v:= f(nn);
if v > N then next fi;
if V[v] = 0 then count:= count+1; V[v]:= nn fi
od:
convert(V, list);
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Jun 08 2022
STATUS
approved