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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. 0
 2, 7, 12, 83408 (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 LINKS 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 Cf. A000040, A071089. Sequence in context: A046243 A230302 A230637 * A103886 A231900 A323740 Adjacent sequences:  A301849 A301850 A301851 * A301853 A301854 A301855 KEYWORD nonn,more AUTHOR J. M. Bergot, Mar 27 2018 EXTENSIONS a(4) from Michel Marcus, Mar 27 2018 STATUS approved

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Last modified August 8 16:09 EDT 2022. Contains 356015 sequences. (Running on oeis4.)