OFFSET
1,1
COMMENTS
Integers k such that A071089(k) = k.
From Robert Israel, Mar 27 2018: (Start)
No more terms below 10^7.
Heuristically, the probability that k is a term is 1/prime(k) ~ 1/(k log k).
Since Sum_{k>=2} 1/(k log(k)) diverges, there should be infinitely many terms. However, the sum diverges very slowly, so terms may be very sparse: approximately log(log(k)) terms <= k. (End)
No more terms below 10^9. - Michel Marcus, Mar 28 2018
No more terms below 1.44*10^12. - Giovanni Resta, Apr 06 2018
No mroe terms below 10^13. - Lucas A. Brown, May 18 2023
LINKS
Lucas A. Brown, Python program.
EXAMPLE
2 is a term because prime(1)+prime(2) = 5 = 2 mod prime(2).
MAPLE
res:= NULL: p:= 1: s:= 0:
for m from 1 to 10^6 do
p:= nextprime(p);
s:= s+p;
if s mod p = m then res:= res, m fi
od:
res; # Robert Israel, Mar 27 2018
PROG
(PARI) lista(nn)= my(p = 2, s = 2); for (n=1, nn, if ((s % p) == n, print1(n, ", ")); q = nextprime(p+1); s += q; p = q; ); \\ Michel Marcus, Mar 27 2018
CROSSREFS
KEYWORD
nonn,more
AUTHOR
J. M. Bergot, Mar 27 2018
EXTENSIONS
a(4) from Michel Marcus, Mar 27 2018
a(5) from Lucas A. Brown, May 18 2023
STATUS
approved