A225940 Numbers n such that prime(n) divides prime(2*n) + prime(3*n).

1, 4, 67, 84, 88

Offset

1,2

Comments

Almost surely the sequence is finite and complete, since the ratio (p(3n)+p(2n))/p(n) tends to 5 from above. For n = 5*10^9 the ratio is 5.19958, for n = 10^100 we can estimate it as 5.02. - Giovanni Resta, May 22 2013

Links

Table of n, a(n) for n=1..5.

Example

Prime(4)=7 divides prime(8)+prime(12)=19+37=56, so 4 is in the sequence.

Mathematica

Select[Range[100], Divisible[Prime[2#]+Prime[3#], Prime[#]]&] (* Harvey P. Dale, Feb 26 2017 *)

Prog

(C)
#include <stdio.h>
#define TOP (1ULL<<32)
typedef unsigned long long U64;
int main() {
  U64 i, j, k, n=1, *primes = (U64*)malloc(TOP);
  char *c = (char*)malloc(TOP/2);
  memset(c, 0, TOP/2);
  for (primes[0] = 2, i = 3; i < TOP; i+=2)
    if (c[i>>1]==0) {
      primes[n++] = i;
      if ((n%3)==0 && (i+primes[n*2/3-1]) % primes[n/3-1]==0)
        printf("%llu, ", n/3);
      for (j = i*i>>1; j < TOP/2; j += i)  c[j] = 1;
    }
  return 0;
}

Crossrefs

Cf. A000040, A066896.

Sequence in context: A198893 A279886 A048828 * A003360 A367121 A225772

Adjacent sequences: A225937 A225938 A225939 * A225941 A225942 A225943

Keyword

nonn,more

Author

Alex Ratushnyak, May 21 2013

Status

approved