A371694 a(1) = 2; a(n+1) is the larger prime between nextprime(a(n)) and prevprime(a(n)+n-m+1), where m is the number of primes < a(n) that are missing from the sequence.

2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 43, 47, 53, 61, 71, 79, 89, 97, 107, 113, 127, 137, 139, 151, 163, 173, 181, 193, 199, 211, 223, 233, 241, 251, 263, 277, 283, 293, 307, 317, 331, 337, 353, 367, 379, 389, 401, 409, 421, 433, 449, 463, 467, 479, 491, 503

Offset

1,1

Comments

The first missing prime in the sequence is 17. First occurrence of a(n)+n-m < nextprime(a(n)) is at n = 20 (see Examples). It seems that 1/2 < n/(n+m) <= 1 and lim_{n->oo} n/(n+m) = 1/2 (or half of the primes are in this sequence).

Links

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

Example

primes    2 3 5  7 11 13 17 19 23 29 31 37 41 43 ..  97 101 103 107 109 113 127
n         1 2 3  4  5  6     7  8  9    10    11 ..  18          19      20  21
a(n)      2 3 5  7 11 13    19 23 29    37    43 ..  97         107     113 127
m         0 0 0  0  0  0     1  1  1     2     3 ..   7           9      10  10
a(n)+n-m  3 5 8 11 16 19    25 30 37    45    51 .. 108         117     123 138
a(n+1)    3 5 7 11 13 19    23 29 37    43    47 .. 107         113     127 137

Prog

(Python)
from sympy import primerange, prevprime, nextprime; p = 2; b = 0
for n in range(1, 57): print(p, end = ", "); q = max(nextprime(p), prevprime(p + n - b + 1)); m = len(list(primerange(p+1, q))); p = q; b += m

Crossrefs

Cf. A362527.

Sequence in context: A005728 A050437 A096246 * A106639 A233462 A233893

Adjacent sequences: A371691 A371692 A371693 * A371695 A371696 A371697

Keyword

nonn

Author

Ya-Ping Lu, Apr 03 2024

Status

approved