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 1-10 of 10 results.

A084960 Initial prime of a prime chain of length n under the iteration x->5x+4.

Original entry on oeis.org

2, 3, 5, 83, 263, 5333, 5333, 6714497, 42360737, 3757699889, 3757699889, 1431898413161, 5654774136689, 12756824771254199, 184574272412533499
Offset: 1

Views

Author

W. Edwin Clark, Jun 14 2003

Keywords

Comments

This is a special case of prime chains generated by f(x) = c*x + d.

Examples

			a(3) = 5 since 5, f(5) = 29 and f(29) = 149 are primes when f(x) = 5x+4.

Links

Crossrefs

Cf. A057330, A057331, A083388, A084954, A084955, A084956, A084957, A084958, A084959, A084961.

Programs

  • Mathematica
    t[p_] := Block[{c=1, q = 5*p+4}, While[ PrimeQ@q, q = 5*q + 4; c++]; c]; a[n_] := Block[{p = 2}, While[t[p] < n, p = NextPrime@ p]; p]; Array[a, 8] (* Giovanni Resta, Mar 21 2017 *)

Extensions

a(9) from Stefan Steinerberger, May 18 2007
a(10)-a(11) from Donovan Johnson, Sep 27 2008
a(12)-a(13) from Giovanni Resta, Mar 21 2017
a(14)-a(15) from Bert Dobbelaere, May 30 2025

A084955 Initial prime of a prime chain of length n under the iteration x->2x+5.

Original entry on oeis.org

2, 3, 7, 13, 13, 13, 541, 4594309, 64649503, 7577449963, 2005324830163, 39676048812109, 272235769110157, 494535766350049
Offset: 1

Views

Author

W. Edwin Clark, Jun 14 2003

Keywords

Comments

This is a special case of prime chains generated by f(x) = cx + d.

Examples

			a(3)=7 since 7, 2*7+5=19 and 2*19+5=43 are primes.

Links

Crossrefs

Cf. A084954.

Extensions

More terms from Don Reble, Nov 07 2007

A084958 Initial prime of a prime chain of length n under the iteration x->5x+2.

Original entry on oeis.org

2, 3, 13, 19, 373, 135859, 135859, 18235423, 26588257, 93112729, 376038903103, 7087694466289, 120223669028389
Offset: 1

Views

Author

W. Edwin Clark, Jun 14 2003

Keywords

Comments

This is a special case of prime chains generated by f(x) = cx + d.
a(11) > 8695354111. - Donovan Johnson, Sep 27 2008

Examples

			a(3)=13 since 13, f(13)=67 and f(67)=337 are primes when f(x) = 5x+2.

Links

Crossrefs

Cf. A057330, A057331, A083388, A084954, A084955, A084956, A084957, A084959, A084960, A084961.

Programs

  • Mathematica
    c[p_] := Block[{k = 1, q = 5*p+2}, While[ PrimeQ[q], q = 5*q+2; k++]; k]; a[n_] := Block[{p = 2}, While[c[p] < n, p = NextPrime@ p]; p]; Array[a, 7] (* Giovanni Resta, Mar 21 2017 *)

Extensions

a(10) from Donovan Johnson, Sep 27 2008
a(11)-a(12) from John Cerkan, Jan 20 2017
a(13) from Giovanni Resta, Mar 21 2017

A084956 Initial prime of the first prime chain of length n under the iteration x -> 3x+4.

Original entry on oeis.org

2, 3, 3, 23, 3203, 34613, 165443, 1274803, 26314573, 26314573, 590256673403, 15113026057043, 334156170011893, 3998669569752373
Offset: 1

Views

Author

W. Edwin Clark, Jun 14 2003

Keywords

Comments

This is a special case of prime chains generated by f(x) = cx + d.
a(11) > 8695354111. - Donovan Johnson, Sep 27 2008

Examples

			a(3) = 3 since 3, f(3) = 13 and f(13) = 43 are primes when f(x) = 3*x + 4.

Links

Crossrefs

Cf. A057330, A057331, A083388, A084954, A084955, A084957, A084958, A084959, A084960, A084961.

Programs

  • Mathematica
    c[p_] := Block[{k=1, q=3*p + 4}, While[PrimeQ[q], q=3*q+4; k++]; k]; a[n_] := Block[{p = 2}, While[c[p] < n, p = NextPrime[p]]; p]; Array[a, 7] (* Giovanni Resta, Mar 22 2017 *)

Extensions

a(9)-a(10) from Donovan Johnson, Sep 27 2008
a(11)-a(12) from John Cerkan, Jan 13 2017
a(13)-a(14) from Giovanni Resta, Mar 22 2017

A084957 Initial prime of the first prime chain of length n under the iteration x -> 4x + 3.

Original entry on oeis.org

2, 2, 2, 2, 1447, 9769, 17231, 17231, 32611, 18527009, 161205841, 3123824801, 26813406071, 4398156030379, 4398156030379
Offset: 1

Views

Author

W. Edwin Clark, Jun 14 2003

Keywords

Comments

This is a special case of prime chains generated by f(x) = c*x + d.

Examples

			a(3) = 2 since 2, f(2) = 11, and f(11) = 47 are primes when f(x) = 4*x + 3.

Links

Crossrefs

Cf. A057330, A057331, A083388, A084954, A084955, A084956, A084958, A084959, A084960, A084961.

Programs

  • Mathematica
    c[p_] := Block[{k=1, q=4*p+3}, While[ PrimeQ[q], q=4*q+3; k++]; k]; a[n_] := Block[ {p=2}, While[c[p] < n, p = NextPrime@ p]; p]; Array[a, 9] (* Giovanni Resta, Mar 21 2017 *)
  • PARI
    has(p,n)=for(i=2,n, if(!isprime(p=4*p+3), return(0))); 1
a(n)=forprime(p=2,, if(has(p,n), return(p))) \\ Charles R Greathouse IV, Jan 20 2017

Extensions

a(11)-a(12) from Donovan Johnson, Sep 27 2008
a(13) from John Cerkan, Jan 20 2017
a(14)-a(15) from Giovanni Resta, Mar 21 2017

A084959 Initial prime of a prime chain of length n under the iteration x->5x+6.

Original entry on oeis.org

2, 5, 7, 7, 79, 79, 345431, 21171649, 34640153, 4174239239, 268130051191, 268130051191, 253134809926049, 253134809926049, 253134809926049
Offset: 1

Views

Author

W. Edwin Clark, Jun 14 2003

Keywords

Comments

This is a special case of prime chains generated by f(x) = cx + d.
a(11) > 8695354111. [Donovan Johnson, Sep 27 2008]

Examples

			a(3) = 13 since 7, f(7) = 41, and f(41) = 211 are primes when f(x) = 5*x + 6.

Links

Crossrefs

Cf. A057330, A057331, A083388, A084954, A084955, A084956, A084957, A084958, A084960, A084961.

Programs

  • Mathematica
    c[p_] := Block[{k=1, q = 5*p+6}, While[PrimeQ[q], q = 5*q+6; k++]; k]; a[n_] := Block[{p = 2}, While[c[p] < n, p = NextPrime[p]]; p]; Array[a, 7] (* Giovanni Resta, Mar 22 2017 *)

Extensions

a(7) corrected and a(8)-a(10) from Donovan Johnson, Sep 27 2008
a(11)-a(12) from John Cerkan, Jan 11 2017
a(13)-a(15) from Giovanni Resta, Mar 22 2017

A084961 Initial prime of the first prime chain of length n under the iteration x->6x+5.

Original entry on oeis.org

2, 2, 2, 2, 11, 13, 115571, 23586221, 53165771, 3398453717, 615502598677, 32504183957101, 164289842304587
Offset: 1

Views

Author

W. Edwin Clark, Jun 14 2003

Keywords

Comments

This is a special case of prime chains generated by f(x) = cx + d.
a(11) > 10175130529. [Donovan Johnson, Sep 27 2008]

Examples

			a(3) = 2 since 2, f(2) = 17, and f(17) = 107 are primes when f(x) = 6*x + 5.

Links

Crossrefs

Cf. A057330, A057331, A083388, A084954, A084955, A084956, A084957, A084958, A084959, A084960.

Programs

  • Mathematica
    c[p_] := Block[{k=1, q=6*p+5}, While[ PrimeQ[q], q = 6*q+5; k++]; k]; a[n_] := Block[ {p=2}, While[c[p] < n, p = NextPrime[p]]; p]; Array[a, 7] (* Giovanni Resta, Mar 22 2017 *)

Extensions

a(8)-a(10) from Donovan Johnson, Sep 27 2008
a(11)-a(12) from John Cerkan, Jan 11 2017
a(13) from Giovanni Resta, Mar 22 2017

A128509 Initial prime, greater than 7, of a prime chain of length n under the iteration x -> 2x-7.

Original entry on oeis.org

11, 13, 13, 367, 4987, 9697, 78007, 13356127, 13356127, 6753069187, 218617084627, 35679817649197, 92975416840027
Offset: 1

Views

Author

Zak Seidov, May 07 2007

Keywords

Comments

From the definition we see that the sequence is monotonic (but not strictly) increasing. The sequence is a generalized Cunningham chain. - Stefan Steinerberger, May 12 2007

Examples

			a(2) = 13 because 13, 13*2-7=19 and 19*2-7=31 are primes.

Crossrefs

Cf. A057330, A084954.

Programs

  • Mathematica
    k = 5; For[n = 2, n <= 10, n++, While[Union[PrimeQ[NestList[2# - 7 &, Prime[k], n]], PrimeQ[NestList[2# - 7 &, Prime[k], n]]] != {True}, k++ ]; Print[Prime[k]]] (* Stefan Steinerberger, May 12 2007 *)

Extensions

Edited by Stefan Steinerberger, May 12 2007
Edited by Don Reble, Nov 07 2007

A134701 Smallest initial prime, greater than 3, of a prime chain of length n under the iteration x->2x-3.

Original entry on oeis.org

5, 5, 5, 5, 13, 283, 283, 1823, 443119823, 35332754383, 57704757113, 69478435945493, 2235755385712423, 5314285836920063, 300677829503061013
Offset: 1

Views

Author

Don Reble, Nov 07 2007

Keywords

Examples

			a(3) = 5 because 5, 5*2-3=7, 7*2-3=11 and 11*2-3=19 are primes.

Crossrefs

Cf. A084954.

Extensions

a(14)-a(15) from Bert Dobbelaere, May 28 2025

A134702 Initial prime, greater than 5, of a prime chain of length n under the iteration x->2x-5.

Original entry on oeis.org

7, 11, 11, 11, 11, 11, 11, 11, 29614931, 29614931, 1172182334669, 67667595358511, 124204021800149
Offset: 1

Views

Author

Don Reble, Nov 07 2007

Keywords

Examples

			a(3) = 11 because 11 11*2-5=17 and 17*2-5=29 are primes.

Crossrefs

Cf. A084954.
Showing 1-10 of 10 results.

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