A386275 First term of the first occurrence of a run of exactly n consecutive terms in A072225.

13, 22, 3, 137, 7, 5454, 31076, 8744076, 697642916, 23169509240, 29165083170, 10658896243375

Offset: 1

Author

Kevin Ryde, Jul 25 2025

Keywords

• nonn
• more

Comments

Exactly n means the run is maximal in the sense that it has no further consecutive term before or after.

Prime Puzzles 798 (see links) considers where runs of consecutive terms occur in A072225 (and similar) and terms here through to n=11 are per row n=3, and extra i with g(3,i)=11, of the minimal i table by Vladimir Chirkov.

a(13) and beyond are > 10658896243375 = a(12).

Examples

			For n=4, the first run of 4 consecutive terms in A072225 begins at its term 137 so that a(4) = 137,
  A072225 = ..., 134, 137, 138, 139, 140, 144
                      \----------------/
                      n=4 consecutive maximal run
The n+2 = 6 primes at prime(137) onwards are 773, 787, 797, 809, 811, 821 and the sum of any consecutive 3 of them is a prime.
		

Links

• Carlos Rivera, Puzzle 798. A nice puzzle by Kamenetski, The Prime Puzzles & Problems Connection.
• Kevin Ryde, C Code

Crossrefs

Cf. A072225.

Programs

C

/* See links. */