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A301852 Integers k such that the remainder of the sum of the first k primes divided by the k-th prime is equal to k. 1
2, 7, 12, 83408, 5290146169416 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A046243 A230302 A230637 * A103886 A231900 A323740
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

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Last modified March 2 05:08 EST 2024. Contains 370460 sequences. (Running on oeis4.)