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 1-8 of 8 results.

A228575 Pseudoprimes n to base 2 such that n-4, n-2 and n+2 are primes.

Original entry on oeis.org

645, 656601, 6212361, 18958567881, 287468425245, 626160901281, 1395494019921, 1925525109201, 1960708164801, 1962378065901, 1977370759365, 2788325761551, 3032013857181, 6877227801081, 22298617759881, 30242009317521, 39454593651201, 42401101442001
Offset: 1

Views

Author

Shyam Sunder Gupta, Oct 27 2013

Keywords

Comments

All numbers in this sequence end in either 5 or 1.

Examples

			645 is a pseudoprime (base 2) and 641, 643 and 647 are primes.
		

Crossrefs

A230488 Pseudoprimes n to base 2 such that n-2 and n-4 are primes.

Original entry on oeis.org

645, 33153, 129921, 157641, 451905, 656601, 1608465, 3020361, 3370641, 6212361, 19092921, 34487601, 38790753, 681942801, 940492785, 1109260545, 1574300001, 2693081973, 3037396461, 4160578521, 6424683105, 7384487181, 13671360561, 14966031345, 15731001105
Offset: 1

Views

Author

Shyam Sunder Gupta, Oct 20 2013

Keywords

Examples

			645 is a pseudoprime (base 2) and 643 and 641 are primes.
		

Crossrefs

A230489 Pseudoprimes n to base 2 such that n+2 and n+4 are primes.

Original entry on oeis.org

87249, 831405, 1489665, 2113665, 31880577, 81612105, 84028407, 86559045, 274014885, 1778357505, 1853263365, 2276082537, 9090685605, 12300409857, 43620860865, 69654751377, 248342283645, 634038307449, 848282877345, 1123296404385, 1344952805505, 3307428792777
Offset: 1

Views

Author

Shyam Sunder Gupta, Oct 20 2013

Keywords

Examples

			87249 is a pseudoprime (base 2) and 87251 and 87253 are primes.
		

Crossrefs

A287591 Carmichael numbers k such that k-2 and k+2 are both primes.

Original entry on oeis.org

656601, 25536531021, 8829751133841, 60561233400921, 79934093254401, 352609909731201, 598438077923841, 976515437206401, 2122162714918401, 2789066007968241, 3767175573114801, 7881891474971361, 10740122274670881, 11512252145095521, 16924806963384321
Offset: 1

Views

Author

Amiram Eldar, May 26 2017

Keywords

Comments

Rotkiewicz conjectured that there are infinitely many Carmichael numbers k such that k-2 or k+2 are primes.
The terms were calculated using Pinch's tables of Carmichael numbers (see link below).

Examples

			656601 is in the sequence since it is a Carmichael number (A002997) and both 656599 and 656603 are primes.
		

Crossrefs

Subsequence of A258801.

A230485 Strong pseudoprimes n to base 2 such that n-2 and n+2 are primes.

Original entry on oeis.org

3465253618401, 44202753561285411, 1640293473202755801, 10623546148468360251
Offset: 1

Views

Author

Shyam Sunder Gupta, Oct 20 2013

Keywords

Comments

For all n, a(n)-2 is in A230810. - M. F. Hasler, Dec 08 2016

Examples

			3465253618401 is a strong pseudoprime (base 2) and 3465253618399 and 3465253618403 are primes.
		

Crossrefs

A230559 Pseudoprimes n to base 2 such that n-2, n+2 and n+4 are primes.

Original entry on oeis.org

634038307449, 4846359321105, 11927878640385, 20835183400305, 34166605315305, 54096163177785, 63154533545265, 88365393281985, 189080281720065, 850943773070385, 917252751841665, 1278728202166185, 1602254869802049, 3742704749436465, 6082185264252945
Offset: 1

Views

Author

Shyam Sunder Gupta, Oct 27 2013

Keywords

Comments

All numbers in this sequence end in either 5 or 9.

Examples

			634038307449 is a pseudoprime (base 2) and 634038307447, 634038307451 and 634038307453 are primes.
		

Crossrefs

A228455 Pseudoprimes n to base 2 such that n-2, n+2, n-4 and n+4 are primes.

Original entry on oeis.org

280743771536011785, 666787209284980785, 1386744766793550165, 6558237049521329745, 11646802313400102465
Offset: 1

Views

Author

Shyam Sunder Gupta, Oct 27 2013

Keywords

Comments

All numbers in this sequence end in 5 because n-4 , n-2 is a twin prime pair and so also is n+2 and n+4.
For all n, a(n) - 4 is in A230668(n). Somewhat surprisingly, all terms of A230668 known so far are of that form. - M. F. Hasler, Dec 08 2016

Examples

			280743771536011785 is a pseudoprime (base 2) and 280743771536011781, 280743771536011783, 280743771536011787 and 280743771536011789 are primes.
		

Crossrefs

A287297 Fermat pseudoprimes n such that n+1 is prime.

Original entry on oeis.org

161038, 9115426, 143742226, 665387746, 1105826338, 3434672242, 11675882626, 16732427362, 18411253246, 81473324626, 85898088046, 98730252226, 134744844466, 136767694402, 161097973246, 183689075122, 315554044786, 553588254766, 778581406786, 1077392692846
Offset: 1

Views

Author

Amiram Eldar, May 26 2017

Keywords

Comments

Kazimierz Szymiczek asked about the existence of such pseudoprimes in 1972 (Problem 42 in Rotkiewicz's book). Rotkiewicz found the first 6 terms. Rotkiewicz also proved that there is no Fermat pseudoprime n such that n-1 is prime.
Subsequence of A006935.

Examples

			161038 is in the sequence since it is a Fermat pseudoprime (2^161038 == 2 (mod 161038)), and 161038 + 1 = 161039 is prime.
		

References

  • Andrzej Rotkiewicz, Pseudoprime Numbers and Their Generalizations, Student Association of the Faculty of Sciences, University of Novi Sad, Novi Sad, Yugoslavia, 1972.

Crossrefs

Showing 1-8 of 8 results.