A225939 Numbers k that divide prime(k) + prime(k-1).

4, 6, 13, 14, 15, 74, 190, 688, 690, 6456, 40082, 251735, 251736, 251738, 399916, 637325, 637326, 637342, 637343, 2582372, 2582434, 4124456, 4124458, 6592686, 10553425, 10553433, 10553818, 27067038, 27067053, 43435902, 69709872, 69709877, 69709945, 69709954, 179992917

Offset: 1

Author

Alex Ratushnyak, May 21 2013

Keywords

• nonn

Examples

			prime(3) + prime(4) = 5+7 = 12, because 12 is divisible by 4, the latter is in the sequence.
prime(5) + prime(6) = 11+13 = 24, because 24 is divisible by 6, the latter is in the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..58 (terms < 1.5*10^12)

Crossrefs

Cf. A001043, A023143, A045924, A066895, A066896.

Programs

C

#include 
#define TOP (1ULL<<32)
int main() {
  unsigned long long i, j, n = 1, prev;
  char *c = (char*)malloc(TOP/2);
  memset(c, 0, TOP/2);
  for (prev = 2, i = 3; i < TOP; i += 2)
    if (c[i>>1]==0) {
      if ((i+prev) % ++n == 0)  printf("%llu, ", n);
      for (prev = i, j = i*i>>1; j < TOP/2; j += i)  c[j] = 1;
    }
  return 0;
}

Mathematica

Select[Range[2,10^4],Divisible[Prime@#+Prime[#-1],#]&] (* Giorgos Kalogeropoulos, Aug 20 2021 *)

Sage

def is_a(n): return (nth_prime(n) + nth_prime(n-1)) % n == 0
filter(is_a, (2..1000))  # Peter Luschny, May 22 2013