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.

User: Jorge Coveiro

Jorge Coveiro's wiki page.

Jorge Coveiro has authored 129 sequences. Here are the ten most recent ones:

A361563 Wagstaff numbers that are of the form 4*k + 1.

Original entry on oeis.org

5, 13, 17, 61, 101, 313, 701, 1709, 2617, 10501, 42737, 95369, 138937, 267017, 374321
Offset: 1

Views

Author

Jorge Coveiro, Mar 15 2023

Keywords

Comments

15135397 is also in the sequence, but may not be the next term.

Links

Crossrefs

Cf. A000978 (Wagstaff numbers), A002144 (primes of form 4*k + 1), A112634, A361562.

Programs

  • Python
    from itertools import count, islice
from sympy import prime, isprime
def A361563_gen(): # generator of terms
    return filter(lambda p: not p&2 and isprime(((1<A361563_list = list(islice(A361563_gen(),7)) # Chai Wah Wu, Mar 21 2023

Formula

Intersection of A000978 and A002144.

A361562 Wagstaff numbers that are of the form 4*k + 3.

Original entry on oeis.org

3, 7, 11, 19, 23, 31, 43, 79, 127, 167, 191, 199, 347, 3539, 5807, 10691, 11279, 12391, 14479, 83339, 117239, 127031, 141079, 269987, 986191, 4031399
Offset: 1

Views

Author

Jorge Coveiro, Mar 15 2023

Keywords

Comments

13347311 and 13372531 are also in the sequence, but may not be the next terms.

Links

Crossrefs

Cf. A000978 (Wagstaff numbers), A002145 (primes of form 4*k+3), A112633, A361563.

Programs

  • Python
    from itertools import count, islice
from sympy import prime, isprime
def A361562_gen(): # generator of terms
    return filter(lambda p: p&2 and isprime(((1<A361562_list = list(islice(A361562_gen(),10)) # Chai Wah Wu, Mar 21 2023

Formula

Intersection of A000978 and A002145.

A359436 Primes p such that (4^p - 2^p + 1)/3 is prime.

Original entry on oeis.org

3, 5, 7, 13, 29, 61, 383, 401, 1637, 1871, 36229, 44771, 44797, 75167
Offset: 1

Views

Author

Jorge Coveiro, Dec 31 2022

Keywords

Comments

Terms > 1871 correspond to probable primes.
Is 9 the only composite k such that (4^k - 2^k + 1)/3 is prime? Checked up to 20000. - Andrew Howroyd, Sep 10 2024

Examples

			3 is a term because 3 is prime and (4^3 - 2^3 + 1)/3 = 19 is also prime.

Crossrefs

Cf. A000978.

Programs

  • PARI
    isok(k)={k%2 && ispseudoprime((4^k - 2^k + 1)/3)}
{ forprime(p=3, 2000, if(isok(p), print1(p, ", "))) } \\ Andrew Howroyd, Dec 31 2022

A344361 Primes p such that (2^p-2)/p - 1 is prime.

Original entry on oeis.org

5, 7, 349, 1123, 25447
Offset: 1

Views

Author

Jorge Coveiro, May 15 2021

Keywords

Comments

a(6) > 1199999, if it exists. - Karl-Heinz Hofmann, Jul 27 2021

Examples

			7 is a term because (2^7-2)/7 - 1 = 17 is prime.

Crossrefs

Cf. A064535, A344360.

Programs

  • PARI
    is(p) = isprime(p) && ispseudoprime((2^p-2)/p-1) \\ Jinyuan Wang, May 15 2021

Extensions

a(5) from Hugo Pfoertner, May 17 2021

A344360 Primes p such that (2^p - 2)/p + 1 is prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 53, 67, 83, 167, 1367, 2473, 4789, 34127, 219217
Offset: 1

Views

Author

Jorge Coveiro, May 15 2021

Keywords

Comments

a(15) > 1099997, if it exists. - Karl-Heinz Hofmann, Jul 27 2021
These are primes p such that 2^((2^p-2)/p) == 1 (mod (2^p-2)/p+1) if and only if there are no pseudoprimes of the form (2^q-2)/q+1 with q prime. - Thomas Ordowski, Aug 29 2021

Examples

			7 is a term because (2^7 - 2)/7 + 1 = 19 is prime.

Crossrefs

Cf. A064535, A344361.

Programs

  • Mathematica
    Select[Prime@ Range[10^3], PrimeQ[(2^# - 2)/# + 1] &] (* Michael De Vlieger, Oct 12 2021 *)
  • PARI
    lista(lim)={forprime(p=1,lim,if(ispseudoprime((2^p-2)/p+1), print1(p,", ")))}
  • PARI
    c3(p) = {s=3; for(x=1, p, s=(s^2)%((2^p-2)/p+1)); if(s==9, print1(p, ", "))} /* PRP Test */

Extensions

a(14) from Karl-Heinz Hofmann, Jun 11 2021

A119388 Numbers n such that n == -1 (mod phi(n-1)).

Original entry on oeis.org

2, 3, 5, 7, 11, 31, 71, 511, 2591, 131071, 3359231, 167247871, 8589934591
Offset: 1

Views

Author

Jorge Coveiro, Jul 25 2006

Keywords

Comments

This sequence has the terms from A067933 (all primes), plus 511 and 3359231 that are not primes.
Checked up to x<70000000
a(14) > 10^11. [From Donovan Johnson, Aug 08 2010]

Crossrefs

Cf. A067933.

Programs

  • PARI
    for(x=1,70000000,if(((x)+1)%eulerphi((x)-1)==0,print((x))))

Extensions

a(13) from Donovan Johnson, Aug 08 2010

A119417 Partial sums of A119385.

Original entry on oeis.org

0, 46, 102, 168, 244, 330, 426, 532, 648, 774, 901, 901, 902, 904, 907, 911, 916, 922, 929, 937, 946, 957, 1023, 1099, 1185, 1281, 1387, 1503, 1629, 1765, 1902, 1902, 1904, 1907, 1911, 1916, 1922, 1929, 1937, 1946, 1956, 1968, 2044, 2130, 2226, 2332, 2448
Offset: 0

Views

Author

Jorge Coveiro, Jul 25 2006

Keywords

Programs

Extensions

More terms from R. J. Mathar, Jan 21 2008

A119531 Primes in A000337.

Original entry on oeis.org

5, 17, 769, 3489660929, 112589990684262401, 1945555039024054273, 193428131138340667952988161
Offset: 1

Views

Author

Jorge Coveiro, Jul 27 2006

Keywords

Comments

Next two terms are too big to include, see A128001.

Formula

a(n) = A000337(A128001(n)). - R. J. Mathar, Oct 10 2011

Extensions

Clearer (but incorrect) definition from R. J. Mathar, Jan 27 2008, corrected Oct 10 2011

A119642 Indices of prime numbers of trees with n unlabeled nodes.

Original entry on oeis.org

4, 5, 7, 8, 9, 13, 15, 52, 82, 134, 216, 341, 538, 1414, 17306, 17582
Offset: 1

Views

Author

Jorge Coveiro, Jul 27 2006

Keywords

Comments

No other terms below 40000. - Vaclav Kotesovec, Jul 08 2020

Crossrefs

Cf. A000055, A051420, A119641, A336042.

Formula

A000055(a(n)) = A119641(n). - Amiram Eldar, Apr 22 2018

Extensions

Offset changed by Michel Marcus, Apr 22 2018
a(13)-a(16) from Amiram Eldar, Apr 22 2018

A119641 Prime numbers of trees with n unlabeled nodes.

Original entry on oeis.org

2, 3, 11, 23, 47, 1301, 7741, 83453838443384019701, 3497830604170469202903845457503189, 3043448204076362393100321053325760617159315927820231750001
Offset: 1

Views

Author

Jorge Coveiro, Jul 27 2006

Keywords

Crossrefs

Cf. A000055, A119642.

Formula

A000040 INTERSECTION A000055.
a(n) = A000055(A119642(n)). - Amiram Eldar, Apr 22 2018

Extensions

Offset changed by Michel Marcus, Apr 23 2018

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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