A236443 Primes which start a Cunningham chain of length 4 where every entity of the chain is smallest of twin prime.

253679, 1138829, 58680929, 90895769, 124253009, 269877299, 392071679, 613813199, 1014342209, 1277981669, 1413015029, 1453978679, 1753585679, 2919331379, 3424037189, 3538972709, 4025789039, 4175762009, 4362439199, 4843208789, 5708418869, 5795508599

Offset

1,1

Comments

a(n) generates a Cunningham chain of length 4 and a_n(i) + 2 is also prime for i = 1,2,3 and 4.

This sequence is infinite under Dickson's conjecture. - Charles R Greathouse IV, Jan 29 2014

Terms are congruent to -1 mod 210. - David Radcliffe, Aug 06 2025

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Chris Caldwell, Cunningham chain

Example

a(1)=253679, with associated Cunningham chain 253679, 507359, 1014719, 2029439, all of which are the lower member of a pair of twin primes.

Prog

(Python)
from sympy import isprime
def is_A236443(n):
    return (isprime(n) and isprime(n+2) and isprime(2*n+1) and isprime(2*n+3) and
            isprime(4*n+3) and isprime(4*n+5) and isprime(8*n+7) and isprime(8*n+9))
print([n for n in range(209, 10**9, 210) if is_A236443(n)]) # David Radcliffe, Aug 06 2025
(PARI) is(n)=n%210==209 && isprime(n) && isprime(n+2) && isprime(2*n+1) && isprime(2*n+3) && isprime(4*n+3) && isprime(4*n+5) && isprime(8*n+7) && isprime(8*n+9)
forstep(n=419, 1e9, [1470, 420, 420], if(is(n), print(n))) \\ Charles R Greathouse IV, Jan 29 2014

Crossrefs

Cf. A178421, A005602, A059763.

Sequence in context: A236874 A236163 A140967 * A069176 A253725 A140079

Adjacent sequences: A236440 A236441 A236442 * A236444 A236445 A236446

Keyword

nonn

Author

Abhiram R Devesh, Jan 26 2014

Extensions

More terms from T. D. Noe, Jan 29 2014

Status

approved