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.

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A289564 Primes of the form k!4+512, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

557, 743, 1097, 10457, 66347, 209357, 151413137, 1267390097, 4996617137, 44358635987, 2442358029135994033940387, 654019644904558303836431802744185605453637, 7767791322531438974665300521192692435966766137
Offset: 1

Views

Author

Robert Price, Sep 02 2017

Keywords

Comments

The next term has 190 digits. - Harvey P. Dale, Aug 02 2022

Links

Crossrefs

Cf. A291350.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 512, {i, 0, 100}], PrimeQ[#]&]
Select[Table[Times@@Range[n,1,-4]+512,{n,200}],PrimeQ] (* Harvey P. Dale, Aug 02 2022 *)

A289702 Primes of the form k!4+1024, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

1069, 1609, 1515229, 40884559, 4996617649, 3496303289505049, 3080000333445961551649, 56064899053039198176082552869866162894943516649, 4767836158257635361854381088929485809336884933170042099072266649
Offset: 1

Views

Author

Robert Price, Sep 02 2017

Keywords

Links

Crossrefs

Cf. A291351.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] + 1024, {i, 0, 100}], PrimeQ[#]&]

A289860 Primes of the form k!4 - 2, where k!4 is the quadruple factorial number (A007662).

Original entry on oeis.org

2, 3, 19, 43, 229, 3463, 208843, 5221123, 151412623, 16713607661375623, 1027438963906784290227656915623, 7419136758370889359733910587728123, 64138437276116338514899657030909640623, 99213846986734491072350087622336908512964418837890623
Offset: 1

Views

Author

Robert Price, Jul 13 2017

Keywords

Links

Crossrefs

Cf. A007662, A283554.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n<1, 1, n*MultiFactorial[n-k, k]];
Select[Table[MultiFactorial[i, 4] - 2, {i, 3, 100}], PrimeQ[#]&]

Formula

a(n) = A007662(A283554(n)) - 2. - Elmo R. Oliveira, Feb 25 2025

A291122 Numbers k such that k!4 + 2^2 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

0, 1, 3, 15, 17, 19, 23, 25, 27, 29, 35, 49, 63, 79, 87, 105, 139, 319, 339, 409, 441, 477, 1023, 1107, 1517, 1557, 1625, 4215, 5297, 6291, 6499, 7357, 11639, 12963, 13989, 15825, 19993, 20535, 35391, 58483, 69247
Offset: 1

Views

Author

Robert Price, Aug 17 2017

Keywords

Comments

Corresponding primes are: 5, 5, 7, 3469, 9949, 65839, 1514209, 5221129, 40883539, ...
a(42) > 10^5.
Terms > 35 correspond to probable primes.

Examples

			15!4 + 2^2 = 15*11*7*3*1 + 4 = 3469 is prime, so 15 is in the sequence.

Links

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^2] &]
Select[Range[0,4300],PrimeQ[Times@@Range[#,1,-4]+4]&] (* The program generates the first 28 terms of the sequence. *) (* Harvey P. Dale, Sep 16 2024 *)

Extensions

a(40)-a(41) from Robert Price, Sep 25 2019

A291343 Numbers k such that k!4 + 2^3 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

3, 5, 7, 9, 11, 13, 19, 23, 25, 33, 39, 41, 63, 67, 71, 85, 87, 91, 133, 171, 243, 291, 1239, 1543, 1879, 2169, 2421, 3149, 3323, 3377, 3501, 3529, 5433, 5599, 7299, 11227, 11275, 13939, 27147, 32435, 86455, 92105
Offset: 1

Views

Author

Robert Price, Aug 22 2017

Keywords

Comments

Corresponding primes are: 11, 13, 29, 53, 239, 593, 65843, 1514213, 5221133, ...
a(43) > 10^5.
Terms > 33 correspond to probable primes.

Examples

			13!4 + 2^3 = 13*9*5*1 + 8 = 593 is prime, so 13 is in the sequence.

Links

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^3] &]
Select[Range[100000],PrimeQ[Times@@Range[#,1,-4]+8]&] (* Harvey P. Dale, Oct 29 2022 *)

Extensions

a(41)-a(42) from Robert Price, Sep 25 2019

A291344 Numbers k such that k!4 + 2^4 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

0, 1, 3, 7, 9, 13, 19, 27, 35, 37, 65, 67, 75, 83, 89, 101, 111, 229, 363, 633, 1605, 1663, 1769, 1863, 1947, 2695, 3003, 5309, 7835, 9495, 9945, 11041, 18833, 21119, 21465, 21889, 24509, 26757, 27595, 33657, 54007, 67699, 87915
Offset: 1

Views

Author

Robert Price, Aug 22 2017

Keywords

Comments

Corresponding primes are: 17, 17, 19, 37, 61, 601, 65851, 40883551, ...
a(44) > 10^5.
Terms > 37 correspond to probable primes.

Examples

			13!4 + 2^4 = 13*9*5*1 + 16 = 601 is prime, so 13 is in the sequence.

Links

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^4] &]

Extensions

a(41)-a(43) from Robert Price, Sep 25 2019

A291345 Numbers k such that k!4 + 2^5 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

5, 7, 11, 13, 19, 21, 25, 27, 35, 37, 51, 55, 65, 71, 105, 107, 129, 223, 229, 273, 307, 337, 345, 479, 509, 517, 519, 921, 963, 993, 1309, 1697, 1855, 1871, 2451, 2573, 2755, 3059, 3271, 4005, 4823, 17079, 20209, 20559, 37845, 38343, 68383, 79617, 81539
Offset: 1

Views

Author

Robert Price, Aug 22 2017

Keywords

Comments

Corresponding primes are: 37, 53, 263, 617, 65867, 208877, 5221157, 40883567, ...
a(50) > 10^5.
Terms > 37 correspond to probable primes.

Examples

			13!4 + 2^5 = 13*9*5*1 + 32 = 617 is prime, so 13 is in the sequence.

Links

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^5] &]
Select[Range[82000],PrimeQ[Times@@Range[#,1,-4]+32]&] (* Harvey P. Dale, Apr 11 2022 *)

Extensions

a(47)-a(49) from Robert Price, Sep 25 2019

A291347 Numbers k such that k!4 + 2^6 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

3, 9, 15, 17, 19, 29, 31, 45, 55, 63, 73, 101, 135, 173, 217, 271, 439, 535, 729, 787, 933, 1473, 1651, 6617, 7805, 12461, 13253, 18627, 20243, 55271
Offset: 1

Views

Author

Robert Price, Aug 22 2017

Keywords

Comments

Corresponding primes are: 67, 109, 3529, 10009, 65899, 151412689, 1267389649, ...
a(31) > 10^5.
Terms > 31 correspond to probable primes.

Examples

			15!4 + 2^6 = 15*11*7*3*1 + 64 = 3529 is prime, so 15 is in the sequence.

Links

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^6] &]

Extensions

a(30) from Robert Price, Sep 25 2019

A291348 Numbers k such that k!4 + 2^7 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

3, 7, 9, 11, 15, 19, 29, 37, 91, 123, 151, 197, 415, 763, 1817, 2981, 3977, 4199, 11667, 12865, 16873, 19449, 27213, 31581, 64877, 65401
Offset: 1

Views

Author

Robert Price, Aug 22 2017

Keywords

Comments

Corresponding primes are: 131, 149, 173, 359, 3593, 65963, 151412753, ...
a(27) > 10^5.
Terms > 37 correspond to probable primes.

Examples

			15!4 + 2^7 = 15*11*7*3*1 + 128 = 3593 is prime, so 15 is in the sequence.

Links

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^7] &]
Select[Range[3000],PrimeQ[Times@@Range[#,1,-4]+128]&] (* Harvey P. Dale, Feb 26 2023 *)

Extensions

a(25)-a(26) from Robert Price, Sep 25 2019

A291349 Numbers k such that k!4 + 2^8 is prime, where k!4 = k!!!! is the quadruple factorial number (A007662).

Original entry on oeis.org

1, 7, 11, 31, 57, 73, 97, 105, 209, 245, 403, 545, 917, 953, 1177, 1239, 1283, 1627, 2465, 3701, 4479, 4637, 6349, 7983, 11155, 13595, 15547, 17031, 17609, 24087, 24707, 39773, 40407, 63329
Offset: 1

Views

Author

Robert Price, Aug 22 2017

Keywords

Comments

Corresponding primes are: 257, 277, 487, 1267389841, ...
a(35) > 10^5.
Terms > 31 correspond to probable primes.

Examples

			11!4 + 2^8 = 11*7*3*1 + 256 = 487 is prime, so 11 is in the sequence.

Links

Crossrefs

Cf. A007662, A037082, A084438, A123910, A242994.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 50000], PrimeQ[MultiFactorial[#, 4] + 2^8] &]

Extensions

a(34) from Robert Price, Sep 25 2019
Previous Showing 11-20 of 63 results. Next

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