A089531 -id:A089531 - cp's OEIS frontend

A272476 a(n) = n if n is prime, a(n) = 2*n+3 otherwise.

3, 5, 2, 3, 11, 5, 15, 7, 19, 21, 23, 11, 27, 13, 31, 33, 35, 17, 39, 19, 43, 45, 47, 23, 51, 53, 55, 57, 59, 29, 63, 31, 67, 69, 71, 73, 75, 37, 79, 81, 83, 41, 87, 43, 91, 93, 95, 47, 99, 101, 103, 105, 107, 53, 111, 113, 115, 117, 119, 59, 123, 61, 127

Offset: 0

Vincenzo Librandi, May 02 2016

Prime numbers repeated: 3, 5, 11, 19, 23, 31, 43, 47, 53, 59, 67, 71, ..., that is A065091 without A089531.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Cf. A000040, A018252.

Cf. A061397, A191558.

[IsPrime(n) select n else 2*n+3: n in [0..80]];

Table[If[PrimeQ[n], n, 2 n + 3], {n, 0, 150}]

A274465 Primes which are the sum of cousin prime pairs - 1.

Original entry on oeis.org

17, 29, 41, 89, 137, 197, 257, 389, 449, 461, 557, 617, 701, 761, 797, 881, 929, 977, 1229, 1289, 1481, 1709, 1721, 1877, 2609, 2861, 2897, 2969, 3137, 3221, 3329, 3389, 3989, 4001, 4409, 4481, 4877, 5081, 5237, 5381, 5417, 5501, 5669, 5717, 6329, 6689, 6917, 7229

Offset: 1

Debapriyay Mukhopadhyay, Jun 24 2016

nonn

Cousin primes are prime pairs that differ by 4. Any prime p in this sequence is such that p = (p-3)/2 + (p+5)/2 - 1, where (p-3)/2 and (p+5)/2 are also primes and they differ by 4.
Proper subset of A040117 (e.g., 5 isn't in the sequence). - David A. Corneth, Jun 24 2016
Intersection of A145471 and A089531. - Michel Marcus, Jun 27 2016
Subsequence of A072669. - Michel Marcus, Jun 27 2016

			17 = 7 + 11 - 1. Note that, (17-3)/2 = 7 and (17+5)/2 = 11 and 7, 11 are cousin prime pairs.
29 = 13 + 17 - 1. Note that, (29-3)/2 = 13 and (29+5)/2 = 17 and 13, 17 are cousin prime pairs.
41 = 19 + 23 - 1. Note that, (41-3)/2 = 19 and (41+5)/2 = 23 and 19, 23 are cousin prime pairs.
89 = 43 + 47 - 1. Note that, (89-3)/2 = 43 and (89+5)/2 = 47 and 43, 47 are cousin prime pairs.

John Cerkan, Table of n, a(n) for n = 1..10000

Cf. A023200, A152091, A040117, A145471, A089531, A072669.

Select[2 # + 3 &@ Select[Prime@ Range@ 512, PrimeQ[# + 4] &], PrimeQ] (* Michael De Vlieger, Jun 26 2016 *)

is(n) = isprime(n) && isprime((n-3)/2) && isprime((n+5)/2) \\ David A. Corneth, Jun 24 2016

use ntheory ":all"; say for grep{is_prime($)} map { $+$+4-1 } sieve_prime_cluster(1,5e8,4) # _Dana Jacobsen, Apr 27 2017

A386873 Smallest prime p such that (p-k-1)/k is also prime for all k=1..n.

Original entry on oeis.org

5, 7, 13, 13, 2129401, 62198641, 62198641, 62198641, 28641897012961, 5193520377811921, 64090546658938801

Offset: 1

Marc Morgenegg, Aug 06 2025

All terms are the larger member of a twin prime pair, since for k=1 (p-1-1)/1=p-2 must be prime.

			a(4) = 13 is the smallest prime p such that (p-k-1)/k is prime for all k=1..4. (13-2)/1=11, (13-3)/2=5, (13-4)/3=3, (13-5)/4=2.

Marc Morgenegg, Python Program

Subsequence of A006512.

Cf. A089531.

from itertools import islice
from gmpy2 import is_prime, next_prime
def agen(): # generator of terms
    n = p = 1
    while True:
        k, p = 1, next_prime(p); q, r = p - 2, 0
        while r == 0 and is_prime(q): k += 1; q, r = divmod(p - k - 1, k)
        while n < k: n += 1; yield int(p)
print(list(islice(agen(), 8))) # Michael S. Branicky, Aug 14 2025

from itertools import count
from math import lcm
from sympy import isprime
def A386873(n):
    m = lcm(*range(1,n+1))
    for i in count(m+1,m):
        if isprime(i) and all(isprime((i-1)//j-1) for j in range(1,n+1)):
            return i # Chai Wah Wu, Aug 20 2025

a(n) == 1 mod lcm(1,2,...,n). - Chai Wah Wu, Aug 20 2025

a(9)-a(11) from Jinyuan Wang, Aug 15 2025

cp's OEIS Frontend

A272476 a(n) = n if n is prime, a(n) = 2*n+3 otherwise.

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A274465 Primes which are the sum of cousin prime pairs - 1.

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A386873 Smallest prime p such that (p-k-1)/k is also prime for all k=1..n.

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