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 18 results. Next

A129225 Residues of the Lucas - Lehmer primality test for M(29) = 536870911.

Original entry on oeis.org

4, 14, 194, 37634, 342576132, 250734296, 433300702, 16341479, 49808751, 57936161, 211467447, 71320725, 91230447, 153832672, 217471443, 239636427, 223645010, 90243197, 27374393, 490737401, 35441039, 303927542, 202574536
Offset: 0

Views

Author

Sergio Pimentel, Apr 04 2007

Keywords

Comments

Since a(27) > 0, M(29) = 536870911 is composite. Mersenne numbers are only prime if a(p-2) = 0.

Examples

			a(27) = 365171774^2 - 2 mod 536870911 = 458738443.

Links

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129221, A129222, A129223, A129224, A129226, A001348.

Programs

  • Mathematica
    NestList[Mod[#^2-2, 2^29-1] &, 4, 27] (* Ben Whitmore, Dec 28 2024 *)

Formula

a(0) = 4, a(n) = a(n-1)^2 - 2 mod 2^p-1, last term: a(p-2).

A129219 Residues of the Lucas - Lehmer primality test for M(7) = 127.

Original entry on oeis.org

4, 14, 67, 42, 111, 0
Offset: 0

Views

Author

Sergio Pimentel, Apr 04 2007

Keywords

Comments

Since a(5) = 0, M(7) is prime.

Examples

			a(5)= 111^2 - 2 mod 127 = 0

Links

Crossrefs

Cf. A095847, A003010, A129220, A129221, A129222, A129223, A129224, A129225, A129226.

Formula

a(0) = 4, a(n) = a(n-1)^2 mod 2^p-1. Last term: a(p-2).

A129220 Residues of the Lucas - Lehmer primality test for M(11) = 2047.

Original entry on oeis.org

4, 14, 194, 788, 701, 119, 1877, 240, 282, 1736
Offset: 0

Views

Author

Sergio Pimentel, Apr 05 2007

Keywords

Comments

Since a(9) > 0, M(11) is composite. In fact, 2047 = 23 * 89

Examples

			a(9) = a(8)^2 - 2 mod 2047 = 282^2 - 2 mod 2047 = 1736.

Links

Crossrefs

Cf. A095847, A003010, A129218, A129219, A129221, A129222, A129223, A129224, A129225, A129226, A001348.

Formula

a(0) = 4; a(n) = a(n-1)^2-2 mod 2^p-1. Last term: a(p-2).

Extensions

Offset corrected by Nathaniel Johnston, May 31 2011

A129221 Residues of the Lucas - Lehmer primality test for M(13) = 8191.

Original entry on oeis.org

4, 14, 194, 4870, 3953, 5970, 1857, 36, 1294, 3470, 128, 0
Offset: 0

Views

Author

Sergio Pimentel, Apr 04 2007

Keywords

Comments

Since a(11) = 0, M(13) = 8191 is prime.

Examples

			a(11)= 128^2 - 2 mod 8191 = 16382 mod 8191 = 0

Links

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129222, A129223, A129224, A129225, A129226, A001348.

Formula

a(0) = 4 a(n) = a(n-1)^2 mod 2^p-1 Last term: a(p-2)

A129222 Residues of the Lucas - Lehmer primality test for M(17) = 131071.

Original entry on oeis.org

4, 14, 194, 37634, 95799, 119121, 66179, 53645, 122218, 126220, 70490, 69559, 99585, 78221, 130559, 0
Offset: 0

Views

Author

Sergio Pimentel, Apr 04 2007

Keywords

Comments

Since a(15) = 0, M(17) = 131071 is prime.

Examples

			a(15) = 130559^2 - 2 mod 131071 = 0.

Links

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129221, A129223, A129224, A129225, A129226, A001348.

Formula

a(0) = 4, a(n) = a(n-1)^2 mod 2^p-1. Last term: a(p-2).

A129223 Residues of the Lucas - Lehmer primality test for M(19) = 524287.

Original entry on oeis.org

4, 14, 194, 37634, 218767, 510066, 386344, 323156, 218526, 504140, 103469, 417706, 307417, 382989, 275842, 85226, 523263, 0
Offset: 0

Views

Author

Sergio Pimentel, Apr 04 2007

Keywords

Comments

Since a(17) = 0, M(19) = 524287 is prime.

Examples

			a(17) = 523263^2 - 2 mod 524287 = 0.

Links

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129221, A129222, A129224, A129225, A129226, A001348.

Formula

a(0) = 4, a(n) = a(n-1)^2 mod 2^p-1. Last term: a(p-2).

A129224 Residues of the Lucas - Lehmer primality test for M(23) = 8388607.

Original entry on oeis.org

4, 14, 194, 37634, 7031978, 7033660, 1176429, 7643358, 3179743, 2694768, 763525, 4182158, 7004001, 1531454, 5888805, 1140622, 4321431, 7041324, 2756392, 1280050, 6563009, 6107895
Offset: 0

Views

Author

Sergio Pimentel, Apr 04 2007

Keywords

Comments

Since a(21) > 0, M(23) = 8388607 is composite. Mersenne numbers are only prime if a(p-2) = 0.

Examples

			a(21) = 6563009^2 - 2 mod 8388607 = 6107895.

Links

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129221, A129222, A129223, A129225, A129226, A001348.

Formula

a(0) = 4, a(n) = a(n-1)^2 mod 2^p-1. Last term: a(p-2).

A129226 Residues of the Lucas - Lehmer primality test for M(31) = 2147483647.

Original entry on oeis.org

4, 14, 194, 37634, 1416317954, 669670838, 1937259419, 425413602, 842014276, 12692426, 2044502122, 1119438707, 1190075270, 1450757861, 877666528, 630853853, 940321271, 512995887, 692931217, 1883625615, 1992425718
Offset: 0

Views

Author

Sergio Pimentel, Apr 04 2007

Keywords

Comments

Since a(29) = 0, M(31) = 2147483647 is prime. Mersenne numbers are only prime if a(p-2) = 0.

Examples

			a(29) = 65536^2 - 2 mod 2147483647 = 0.

Links

Crossrefs

Cf. A095847, A003010, A129219, A129220, A129221, A129222, A129223, A129224, A129225, A001348.

Programs

  • Python
    p = 31; Mp = 2**p - 1
from itertools import accumulate
def f(anm1, _): return (anm1**2 - 2) % Mp
print(list(accumulate([4]*30, f))) # Michael S. Branicky, Apr 14 2021

Formula

a(0) = 4, a(n) = a(n-1)^2 mod 2^p-1. Last term: a(p-2).

A131458 Residues of 3^(2^(p(n)-1)-1) for Mersenne numbers with prime indices.

Original entry on oeis.org

0, 6, 30, 126, 1565, 8190, 131070, 524286, 7511964, 89777599, 2147483646, 20166585982, 840455563322, 4787976306682, 5519162753736, 2617809209727498, 334169564069012755, 2305843009213693950, 47306781863857413639
Offset: 1

Views

Author

Dennis Martin (dennis.martin(AT)dptechnology.com), Jul 13 2007, Jul 20 2007

Keywords

Comments

Mp is prime iff 3^(2^(p(n)-1)-1) is congruent to (-1) Mod Mp. Thus M7 = 127 is prime because 3^63 Mod 127 = 126 (=127-1) while M11 = 2047 is composite because 3^1023 Mod 2047 <> 2046.

Examples

			a(5) = 3^(2^(11-1)-1) Mod 2^11-1 = 3^1023 Mod 2047 = 1565

Links

Crossrefs

Cf. A095847, A001348, A131459, A131460, A131461, A131462, A131463.

Formula

a(n) = 3^(2^(p(n)-1)-1) Mod 2^p(n)-1

A131459 Residues of 3^(2^(p(n)-1)) for Mersenne numbers with prime indices.

Original entry on oeis.org

0, 4, 28, 124, 601, 8188, 131068, 524284, 5758678, 269332797, 2147483644, 60499757946, 322343434415, 5567835897839, 16557488261208, 7853427629182494, 426047939903614778, 2305843009213693948, 141920345591572240917
Offset: 1

Views

Author

Dennis Martin (dennis.martin(AT)dptechnology.com), Jul 13 2007, Jul 20 2007

Keywords

Comments

Mp is prime iff 3^(2^(p(n)-1)) is congruent to (-3) Mod Mp. Thus M7 = 127 is prime because 3^64 Mod 127 = 124 (=127-3) while M11 = 2047 is composite because 3^1024 Mod 2047 <> 2044.

Examples

			a(5) = 3^(2^(11-1)) Mod 2^11-1 = 3^1024 Mod 2047 = 601

Links

Crossrefs

Cf. A095847, A001348, A131458, A131460, A131461, A131462, A131463.

Formula

a(n) = 3^(2^(p(n)-1)) Mod 2^p(n)-1
Showing 1-10 of 18 results. Next

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