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 1-9 of 9 results.

A228026 Primes of the form 4^k + 3.

Original entry on oeis.org

7, 19, 67, 4099, 65539, 262147, 268435459, 1073741827, 19342813113834066795298819
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Examples

			67 is a term because 4^3 + 3 = 67 is prime.

Links

Crossrefs

Cf. A089437 (associated k).
Cf. Primes of the form r^k + h: A092506 (r=2, h=1), A057733 (r=2, h=3), A123250 (r=2, h=5), A104066 (r=2, h=7), A104070 (r=2, h=9), A057735 (r=3, h=2), A102903 (r=3, h=4), A102870 (r=3, h=8), A102907 (r=3, h=10), A290200 (r=4, h=1), this sequence (r=4, h=3), A228027 (r=4, h=9), A182330 (r=5, h=2), A228029 (r=5, h=6), A102910 (r=5, h=8), A182331 (r=6, h=1), A104118 (r=6, h=5), A104115 (r=6, h=7), A104065 (r=7, h=4), A228030 (r=7, h=6), A228031 (r=7, h=10), A228032 (r=8, h=3), A228033 (r=8, h=5), A144360 (r=8, h=7), A145440 (r=8, h=9), A228034 (r=9, h=2), A159352 (r=10, h=3), A159031 (r=10, h=7).

Programs

  • Magma
    [a: n in [0..200] | IsPrime(a) where a is  4^n+3];
  • Mathematica
    Select[Table[4^n + 3, {n, 0, 200}], PrimeQ]

Formula

a(n) = 4^A089437(n) + 3. - Elmo R. Oliveira, Nov 14 2023

Extensions

Cross-references corrected by Robert Price, Aug 01 2017

A228032 Primes of the form 8^n + 3.

Original entry on oeis.org

11, 67, 4099, 32771, 262147, 1073741827, 19342813113834066795298819
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Links

Crossrefs

Cf. A217354 (associated n).
Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=8, h=3), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

Programs

  • Magma
    [a: n in [0..300] | IsPrime(a) where a is  8^n+3];
  • Mathematica
    Select[Table[8^n + 3, {n, 0, 300}], PrimeQ]

Extensions

Corrected cross-references - Robert Price, Aug 01 2017

A228029 Primes of the form 5^n + 6.

Original entry on oeis.org

7, 11, 31, 131, 631, 1220703131
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Links

Crossrefs

Cf. A089142 (associated n).
Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), this sequence (k=5, h=6), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

Programs

  • Magma
    [a: n in [0..200] | IsPrime(a) where a is  5^n+6];
  • Mathematica
    Select[Table[5^n + 6, {n, 0, 200}], PrimeQ]

Extensions

Corrected cross-references - Robert Price, Aug 01 2017

A228030 Primes of the form 7^n + 6.

Original entry on oeis.org

7, 13, 349, 33232930569607, 2651730845859653471779023381607
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Links

Crossrefs

Cf. A217130 (associated n).
Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=7, h=6), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

Programs

  • Magma
    [a: n in [0..300] | IsPrime(a) where a is  7^n+6];
  • Mathematica
    Select[Table[7^n + 6, {n, 0, 300}], PrimeQ]

Extensions

Corrected cross-references - Robert Price, Aug 01 2017

A228031 Primes of the form 7^n + 10.

Original entry on oeis.org

11, 17, 59, 353, 2411, 117659, 823553, 1977326753, 9387480337647754305659, 3219905755813179726837617, 44567640326363195900190045974568017, 616873509628062366290756156815389726793178417, 30226801971775055948247051683954096612865741953
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Links

Crossrefs

Cf. A217132 (associated n).
Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=7, h=10), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

Programs

  • Magma
    [a: n in [0..300] | IsPrime(a) where a is  7^n+10];
  • Mathematica
    Select[Table[7^n + 10, {n, 0, 300}], PrimeQ]

Extensions

Corrected cross-references - Robert Price, Aug 01 2017

A228027 Primes of the form 4^k + 9.

Original entry on oeis.org

13, 73, 1033, 262153, 1073741833, 73786976294838206473, 4835703278458516698824713
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Comments

Subsequence of A104070. - Elmo R. Oliveira, Nov 28 2023

Examples

			262153 is a term because 4^9 + 9 = 262153 is prime.

Links

Crossrefs

Cf. A000040, A217350 (corresponding k's).
Cf. Primes of the form r^k + h: A092506 (r=2, h=1), A057733 (r=2, h=3), A123250 (r=2, h=5), A104066 (r=2, h=7), A104070 (r=2, h=9), A057735 (r=3, h=2), A102903 (r=3, h=4), A102870 (r=3, h=8), A102907 (r=3, h=10), A290200 (r=4, h=1), A228026 (r=4, h=3), this sequence (r=4, h=9), A182330 (r=5, h=2), A228029 (r=5, h=6), A102910 (r=5, h=8), A182331 (r=6, h=1), A104118 (r=6, h=5), A104115 (r=6, h=7), A104065 (r=7, h=4), A228030 (r=7, h=6), A228031 (r=7, h=10), A228032 (r=8, h=3), A228033 (r=8, h=5), A144360 (r=8, h=7), A145440 (r=8, h=9), A228034 (r=9, h=2), A159352 (r=10, h=3), A159031 (r=10, h=7).

Programs

  • Magma
    [a: n in [0..200] | IsPrime(a) where a is 4^n+9];
  • Mathematica
    Select[Table[4^n + 9, {n, 0, 200}],PrimeQ]

Formula

a(n) = 4^A217350(n) + 9. - Elmo R. Oliveira, Nov 28 2023

Extensions

Corrected cross-references - Robert Price, Aug 01 2017

A228033 Primes of the form 8^k + 5.

Original entry on oeis.org

13, 2787593149816327892691964784081045188247557, 15177100720513508366558296147058741458143803430094840009779784451085189728165691397
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Comments

a(4) = 8^64655 + 5 = 1.919...*10^58389 is too large to include. - Amiram Eldar, Jul 23 2025

Crossrefs

Cf. A217355 (associated n).
Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A182330 (k=5, h=2), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), this sequence (k=8, h=5), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

Programs

  • Magma
    [a: n in [1..300] | IsPrime(a) where a is 8^n+5];
  • Mathematica
    Select[Table[8^n + 5, {n, 4000}], PrimeQ]

A217382 Numbers k such that 8^k + 9 is prime.

Original entry on oeis.org

1, 2, 3, 6, 10, 19, 22, 109, 798, 1498, 1519, 3109, 5491, 13351, 26983, 48799, 57909, 98109
Offset: 1

Views

Author

Vincenzo Librandi, Oct 03 2012

Keywords

Comments

All terms are equal to 1/3 of the multiples of 3 in A057196.

Crossrefs

Cf. A057196, A217354, A217355.
Cf. A145440 (associated primes).

Programs

  • Mathematica
    Select[Range[10000], PrimeQ[8^# + 9] &]
  • PARI
    is(n)=ispseudoprime(8^n+9) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(16)-a(18) from Michael S. Branicky, May 17 2025 using b-file at A057196

A228028 Primes of the form 5^n + 4.

Original entry on oeis.org

5, 29, 15629, 9765629
Offset: 1

Views

Author

Vincenzo Librandi, Aug 11 2013

Keywords

Links

Crossrefs

Cf. A124621 (associated n).
Cf. Primes of the form k^n + h: A092506 (k=2, h=1), A057733 (k=2, h=3), A123250 (k=2, h=5), A104066 (k=2, h=7), A104070 (k=2, h=9), A057735 (k=3, h=2), A102903 (k=3, h=4), A102870 (k=3, h=8), A102907 (k=3, h=10), A290200 (k=4, h=1), A228027 (k=4, h=9), A182330 (k=5, h=2), this sequence (k=5, h=4), A228029 (k=5, h=6), A102910 (k=5, h=8), A182331 (k=6, h=1), A104118 (k=6, h=5), A104115 (k=6, h=7), A104065 (k=7, h=4), A228030 (k=7, h=6), A228031 (k=7, h=10), A228032 (k=8, h=3), A228033 (k=8, h=5), A144360 (k=8, h=7), A145440 (k=8, h=9), A228034 (k=9, h=2), A159352 (k=10, h=3), A159031 (k=10, h=7).

Programs

  • Magma
    [a: n in [0..200] | IsPrime(a) where a is  5^n+4];
  • Mathematica
    Select[Table[5^n + 4, {n, 0, 200}], PrimeQ]

Extensions

Corrected cross-references - Robert Price, Aug 01 2017
Showing 1-9 of 9 results.

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