A395565 Primes p preceded and followed by primes whose difference is greater than 2*log(p).

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 47, 53, 67, 79, 83, 89, 97, 113, 127, 131, 139, 149, 157, 173, 181, 191, 199, 211, 223, 241, 251, 257, 263, 283, 293, 307, 317, 331, 337, 347, 359, 367, 373, 389, 397, 401, 409, 449, 467, 479, 509, 521, 523, 541, 547

Offset

1,1

Comments

Primes prime(k) such that prime(k+1) - prime(k-1) > 2*log(prime(k)).

Complement of A381850 within primes.

Links

Table of n, a(n) for n=1..56.

Formula

Conjecture: lim_{n->oo} n / pi(a(n)) = 3/e^2.

Example

37 is a term because 41-31=10 and 2*log(37)=7.2218.
41 is not a term because 43-37=6 and 2*log(41)=7.4271.

Mathematica

q[k_]:=NextPrime[k]-NextPrime[k, -1]>2Log[k]; Select[Prime[Range[2, 101]], q] (* James C. McMahon, May 04 2026 *)

Prog

(PARI) forprime(P=3, 500, my(M=precprime(P-1), Q=nextprime(P+1)); if(Q-M>2*log(P), print1(P, ", ")));

Crossrefs

Cf. A000720, A031131, A381850, A383216.

Sequence in context: A165255 A223036 A155058 * A007703 A002556 A376206

Adjacent sequences: A395562 A395563 A395564 * A395566 A395567 A395568

Keyword

nonn

Author

Alain Rocchelli, Apr 28 2026

Status

approved