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 1-7 of 7 results.

A086661 Numbers k such that k*4^k-1 is prime.

Original entry on oeis.org

1, 2, 3, 5, 8, 14, 23, 63, 107, 132, 428, 530, 1137, 1973, 2000, 7064, 20747, 79574, 113570, 293912, 1993191
Offset: 1

Views

Author

Farideh Firoozbakht, Jul 27 2003

Keywords

Comments

2, 3, 5, 23, 107, 1973, 20747 is the subsequence of prime terms.

Examples

			2 is in the sequence because 2*4^2-1=31 is prime.
3 is in the sequence because 3*4^3-1=191 is prime.

References

  • H. Dubner, Generalized Cullen Numbers, J. Rec. Math, 21 (No. 3, 1989).

Links

Crossrefs

Cf. A007646, A002234, A005849.

Programs

  • Mathematica
    Do[If[PrimeQ[n*4^n-1], Print[n]], {n, 4000}]
Select[Range[2000],PrimeQ[# 4^#-1]&] (* Harvey P. Dale, Nov 09 2024 *)
  • PARI
    is(n)=ispseudoprime(n*4^n-1) \\ Charles R Greathouse IV, May 22 2017

Extensions

One more term from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 23 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
Prepended first terms 1 and 2 - Pierre CAMI, Jul 21 2014
a(20)-a(21) from Harvey link by Ray Chandler, Apr 10 2016

A242176 Numbers k such that k*6^k + 1 is prime.

Original entry on oeis.org

1, 2, 91, 185, 387, 488, 747, 800, 9901, 10115, 12043, 13118, 30981, 51496
Offset: 1

Views

Author

Vincenzo Librandi, May 08 2014

Keywords

Links

Crossrefs

Cf. numbers n such that n*k^n + 1 is prime: A005849 (k=2), A006552 (k=3), A007646 (k=4), this sequence (k=6), A242177 (k=7), A242178 (k=8), A007647 (k=10), A242196 (k=12), A242197 (k=14), A242198 (k=15), A242199 (k=16), A007648 (k=18).

Programs

  • Magma
    [n: n in [0..1500] | IsPrime(n*6^n+1)];
  • Mathematica
    Select[Range[1500], PrimeQ[# 6^# + 1] &]
  • PARI
    is(n)=ispseudoprime(n*6^n+1) \\ Charles R Greathouse IV, Feb 17 2017

Extensions

a(9)-a(14) from Loeh's list (see Links) - Bruno Berselli, May 08 2014

A029544 Near Cullen numbers: k such that (k+1)*2^k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 5, 6, 13, 26, 65, 66, 86, 114, 133, 186, 294, 445, 866, 1325, 1478, 1823, 2765, 7553, 7943, 10178, 20960, 20964, 21337, 26562, 85374, 96749, 247038
Offset: 1

Views

Author

Henri Lifchitz

Keywords

Comments

Primes in the sequence are 2, 5, 13, 1823, 96749, ... - R. J. Mathar, Oct 15 2011
We can write (k+1)*2^k + 1 = {(k+1)/2}*4^{(k+1)/2} + 1, and when k is odd, this takes the form of a generalized Cullen prime (base 4). These are listed in A007646. In other words, {2*A007646 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019

Links

Crossrefs

Cf. A002064, A007646, A230769.

Programs

  • PARI
    isok(n) = isprime((n+1)*2^n+1); \\ Michel Marcus, Nov 09 2013

Extensions

Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

A210339 Generalized Cullen primes: any primes that can be written in the form n*b^n + 1 with n+2 > b > 2.

Original entry on oeis.org

19, 193, 52489, 114689, 9000000001, 259374246011, 38280596832649217, 59296646043258913, 408700964355468751, 2434970217729660813313, 13576803638250229989377, 21000000000000000000001, 3140085798164163223281069127, 4818833289797717549937328129
Offset: 1

Views

Author

Arkadiusz Wesolowski, Mar 20 2012

Keywords

Examples

			81*2^324 + 1 is a prime number and 81*2^324 + 1 = 81*16^81 + 1, so this number is in the sequence.

References

  • Harvey Dubner, Generalized Cullen numbers, J. Recreational Math. 21 (1989), pp. 190-194.

Links

Crossrefs

Cf. A050920, A005849, A006552, A007646.

Programs

  • Mathematica
    lst = {}; Do[p = n*b^n + 1; If[p < 10^200 && PrimeQ[p], AppendTo[lst, p]], {b, 3, 100}, {n, b - 1, 413}]; Sort@lst

A242204 Numbers n such that n*4^n+1 is semiprime.

Original entry on oeis.org

2, 6, 8, 9, 13, 15, 25, 36, 37, 63, 66, 72, 73, 85, 205, 333, 430
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2014

Keywords

Comments

The semiprimes of this form are: 33, 24577, 524289, 2359297, 872415233, 16106127361, 28147497671065601, 170005193383307227693057, 698910239464707491627009, ...
a(18) >= 547. - Hugo Pfoertner, Aug 05 2019

Links

Crossrefs

Cf. similar sequences listed in A242203.
Cf. A007646, A050915.

Programs

  • Magma
    IsSemiprime:=func; [n: n in [1..110] | IsSemiprime(s) where s is n*4^n+1];
  • Mathematica
    Select[Range[120], PrimeOmega[# 4^# + 1] == 2 &]

Extensions

a(15)-a(17) from Luke March, Aug 13 2015

A265013 Numbers n such that n*9^n + 1 is prime.

Original entry on oeis.org

2, 12382, 27608, 31330, 117852
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Nov 30 2015

Keywords

Comments

All terms are even. - Robert Israel, Jan 18 2016

Crossrefs

Cf. A005849, A006552, A007646, A242176, A242177, A242178, A007647, A242196, A242197, A242198, A242199, A007648.

Programs

  • Magma
    [n: n in [0..100000] | IsPrime(n*9^n+1)];
  • Mathematica
    Select[Range[100000], PrimeQ[# 9^# + 1] &]
  • PARI
    for(n=1,100000, if(isprime(n*9^n+1), print1(n,", ")))

A338412 Numbers k such that k * 20^k + 1 is prime.

Original entry on oeis.org

3, 6207, 8076, 22356, 151456
Offset: 1

Views

Author

Tim Johannes Ohrtmann, Oct 25 2020

Keywords

Comments

a(6) > 219976.

Links

Crossrefs

Numbers k such that k * b^k + 1 is prime: A006093 (b=1), A005849 (b=2), A006552 (b=3), A007646 (b=4), A242176 (b=6), A242177 (b=7), A242178 (b=8), A265013 (b=9), A007647(b=10), A242196(b=12), A242197 (b=14), A242198 (b=15), A242199 (b=16), A007648 (b=18), this sequence (b=20).

Programs

  • Magma
    [n: n in [1..10000] |IsPrime(n*20^n+1)]
  • Mathematica
    Select[Range[1, 10000], PrimeQ[n*20^n+1] &]
  • PARI
    for(n=1, 10000, if(isprime(n*20^n+1), print1(n, ", ")))
Showing 1-7 of 7 results.

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

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