A337648 Odd primes p such that the first term in A336957 that is divisible by p is 2*p.

3, 19, 59, 73, 83, 89, 127, 131, 137, 149, 151, 157, 163, 193, 223, 227, 229, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491

Offset: 1

Author

N. J. A. Sloane, Sep 26 2020

Keywords

• nonn

Comments

Conjecture 1: this sequence contains all primes > 367.

Conjecture 2: The set of odd primes is partitioned into A337648, A337649, and {7}.

(These conjectures have been checked for the first 161734 terms of A336957.)

When an odd prime p first divides a term of A336957 that term is equal to q*p where q < p is also a prime. It appears q is almost always 2 (the corresponding values of p form the present sequence), that there are 34 instances when q = 3 (see A337649), and q>3 happens just once, at A336957(5) = 35 when q=5 and p=7.

See also the comment in A336957 discussing when primes first appear in A336957.

Crossrefs

Cf. A336957, A337275, A337649.