cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

253679, 1138829, 58680929, 90895769, 124253009, 269877299, 392071679, 613813199, 1014342209, 1277981669, 1413015029, 1453978679, 1753585679, 2919331379, 3424037189, 3538972709, 4025789039, 4175762009, 4362439199, 4843208789, 5708418869, 5795508599
Offset: 1

Views

Author

Abhiram R Devesh, Jan 26 2014

Keywords

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

Examples

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

Links

Crossrefs

Cf. A178421, A005602, A059763.

Programs

  • 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
  • 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

Extensions

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

A237495 Primes which start a Cunningham chain of length 5 where every prime in the chain is the smaller of a pair of twin primes.

Original entry on oeis.org

41887255409, 364223689829, 376655795669, 790031896499, 1558600513469, 2180283962009, 3266149150109, 4424063189699, 4655123392919, 6924093600269, 7706450161409, 9792446379869, 14825914106849, 15049625144399, 15612571518389, 18228407987789, 20440411077239
Offset: 1

Views

Author

Abhiram R Devesh, Feb 08 2014

Keywords

Comments

This is subset of the sequence A236443. Of the first 10000 terms in the sequence A236443 only 48 have length 5.
a(n) generates a Cunningham chain of length 5 and a_n(i) + 2 is also prime for i = 1,2,3,4 and 5.
This sequence is infinite under Dickson's conjecture.

Examples

			a(1) = 41887255409, with associated Cunningham chain of length 5: 41887255409, 83774510819, 167549021639, 335098043279, 670196086559, each of which is the smaller of a pair of twin primes.

Links

Crossrefs

Cf. A178421, A005602, A236443 is a superset of this sequence.

Extensions

a(11)-a(17) from David Radcliffe, Aug 09 2025

A237017 Primes which start a Cunningham chain of length 4 where every entity of the chain is smallest of the prime number pair (p, p+8).

Original entry on oeis.org

359, 1069199, 1392269, 2614169, 10528649, 16981379, 18287309, 19463519, 21071489, 21171509, 22121579, 24857639, 40887569, 41809259, 76130129, 88362479, 118136279, 128893049, 131612609, 153318449, 289743689, 315495539
Offset: 1

Views

Author

Abhiram R Devesh, Feb 02 2014

Keywords

Comments

a(n) generates a Cunningham chain of length 4 and a_n(i) + 8 is also prime for i = 1,2,3 and 4.
This sequence is infinite under Dickson's conjecture.

Examples

			a(1)=359, with associated Cunningham chain 359, 719, 1439, 2879; all of which are the lower member of a pair (p, p+8): (359,367), (719,727), (1439,1447), (2879,2887).

Links

Crossrefs

Cf. A236443, A178421, A005602, A059763.

Programs

  • Python
    from sympy import isprime, primerange
is_a237017 = lambda p: all(isprime(q) for q in (p+8, 2*p+1, 2*p+9, 4*p+3, 4*p+11, 8*p+7, 8*p+15))
print(*[p for p in primerange(10**7) if is_a237017(p)], sep=', ')
# David Radcliffe, May 11 2025
Showing 1-3 of 3 results.

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