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 1-7 of 7 results.

A084954 Initial prime of a prime chain of length n under the iteration x->2x+3.

Original entry on oeis.org

2, 2, 2, 2, 47, 47, 6047, 477727, 30596497, 3388516667, 340746580567, 1763093883977, 773521306107547, 1142275515892937, 391230854658184967
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.
Is it smallest initial prime of a prime chain of length n under the iteration x->2x+3, or not? At least up to 3388516667 it is the smallest one. - Zak Seidov, Dec 20 2013

Examples

			a(3) = 2 since 2, 2*2+3=7 and 2*7+3=17 are primes.

Links

Crossrefs

Cf. A057330, A057331, A083388, A084955, A084956, A084957, A084958, A084959, A084960, A084961, A128509, A134701, A134702.

Extensions

More terms from Don Reble, Nov 07 2007
a(15) from Bert Dobbelaere, Jun 01 2025

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

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

A280720 For p = prime(n), number of iterations of the function f(x) = 5x + 2 that leave p prime.

Original entry on oeis.org

0, 1, 0, 1, 0, 2, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Felix Fröhlich, Jan 07 2017

Keywords

Comments

Records are a(1) = 0 [p = 2], a(2) = 1 [p = 3], a(6) = 2 [p = 13], a(8) = 3 [p = 19], a(74) = 4 [p = 373], a(12656) = 6 [p = 135859], a(1165346) = 7 [p = 18235423], a(1659004) = 8 [p = 26588257], a(5386789) = 9 [p = 93112729], .... - Charles R Greathouse IV, Jan 12 2017

Links

Crossrefs

Cf. A016873, A023217, A023252, A023283, A023313, A023341, A084958, A249573.

Programs

  • Mathematica
    Table[Length@ NestWhileList[5 # + 2 &, Prime@ n, PrimeQ] - 2, {n, 120}] (* Michael De Vlieger, Jan 09 2017 *)
  • PARI
    a016873(n) = 5*n+2
a(n) = my(p=prime(n), i=0); while(1, if(!ispseudoprime(a016873(p)), return(i), p=a016873(p); i++))
Showing 1-7 of 7 results.

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