A387591 Primes prime(k) such that (k+1)*prime(k) < k*prime(k+1).

3, 5, 7, 13, 19, 23, 31, 37, 43, 47, 53, 61, 67, 73, 79, 83, 89, 97, 103, 109, 113, 131, 139, 151, 157, 167, 173, 181, 199, 211, 233, 241, 251, 257, 263, 271, 283, 293, 317, 331, 337, 353, 359, 367, 373, 383, 389, 401, 409, 421, 433, 443, 449, 467, 479, 491, 503, 509, 523, 541, 547, 557, 563, 571, 577, 587, 593, 601, 607, 619

Offset

1,1

Comments

Sequence relates to Erdős problem 968.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Thomas Bloom, Problem 968, Erdős Problems.

Erdős problems database contributors, Erdős problem database, see no. 968.

Maple

f:= k-> (p-> `if`((k+1)*p<k*nextprime(p), p, [][]))(ithprime(k)):
map(f, [$1..114])[];  # Alois P. Heinz, Sep 03 2025

Mathematica

seq[max_] := Module[{p = Prime[Range[max]]}, p[[Position[Rest[p]/Most[p] - (1 + 1/Range[max-1]), _?Positive] // Flatten]]]; seq[115] (* Amiram Eldar, Sep 03 2025 *)

Prog

(Python)
from sympy import nextprime
def A387591_generate():
    k, p_k, p_k_plus_1 = 1, 2, 3
    while True:
        if p_k * (k + 1) < k * p_k_plus_1:
            yield p_k
        k, p_k, p_k_plus_1 = k + 1, p_k_plus_1, nextprime(p_k_plus_1)
print([p_k for _, p_k in zip(range(70), A387591_generate())])
(PARI) isok(p) = if (isprime(p), my(k=primepi(p)); (k+1)*p < k*nextprime(p+1)); \\ Michel Marcus, Sep 03 2025

Crossrefs

A233866 is the complement restricted to Ramanujan primes (A104272).

Sequence in context: A357170 A277717 A120460 * A127459 A174635 A075579

Adjacent sequences: A387588 A387589 A387590 * A387592 A387593 A387594

Keyword

nonn

Author

Vishal Doshi, Sep 02 2025

Status

approved