A225504 a(n) = prime((a(n-1) + a(n-2)) / 2) for n>1, with a(0) = 3, a(1) = 5.

3, 5, 7, 13, 29, 73, 233, 883, 4049, 22013, 140269, 1036183, 8771489, 84270997, 910550899, 10977409981, 146618640533, 2155882170713, 34701120973507, 608312884303213, 11560371513545909, 237170393590520353, 5232858369551752099, 123736201926723358439

Offset

0,1

Links

Table of n, a(n) for n=0..23.

Mathematica

nxt[{a_, b_}] := {b, Prime[(a + b)/2]}; Transpose[NestList[nxt, {3, 5}, 17]][[1]] (* The program generates only the first 18 terms of the sequence; the 19th term is too large for Mathematica to generate it *) (* Harvey P. Dale, Apr 24 2016 *)

Prog

(C)
#include <stdio.h>
#define TOP (1ULL<<32)
typedef unsigned long long U64;
int main() {
  U64 i, j, p = 2, prpr = 3, prev = 5;
  unsigned int *primes = (unsigned int*)malloc(TOP/4);
  char *c = (char*)malloc(TOP/2);
  memset(c, 0, TOP/2);
  for (primes[1] = 2, i = 3; i < TOP; i+=2)
    if (c[i>>1]==0)
      for (primes[p++]=i, j=i*i>>1; j<TOP/2; j+=i) c[j]=1;
  for (printf("3, 5, "); (prev+prpr)/2<p; prpr=prev, prev=i)
    i = primes[(prev+prpr)/2], printf("%llu, ", i);
}

Crossrefs

Cf. A000040, A107327.

Sequence in context: A087383 A038928 A359436 * A089740 A191473 A290482

Adjacent sequences: A225501 A225502 A225503 * A225505 A225506 A225507

Keyword

nonn,hard,more

Author

Alex Ratushnyak, May 09 2013

Extensions

a(15)-a(18) from Max Alekseyev, Jan 30 2014

a(19)-a(23) from Jinyuan Wang, Nov 14 2020

Status

approved