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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A062585 Numbers k such that 19^k - 18^k is prime.

Original entry on oeis.org

2, 1607, 1873, 10957
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

PrimePi[ a(n) ] = {2, 253, 287, 1331, ...}. - Alexander Adamchuk, Feb 16 2007
a(5) > 10^5. - Robert Price, Jun 05 2012
Terms greater than 1000 may correspond to (unproven) strong pseudoprimes. - M. F. Hasler, Sep 16 2013

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062583, A188051, A062586-A062666.

Programs

Extensions

10957 (found by Mike Oakes in 2003) from Alexander Adamchuk, Feb 16 2007

A062583 Numbers k such that 17^k - 16^k is prime.

Original entry on oeis.org

5, 7, 79, 523, 571, 2837
Offset: 1

Views

Author

Mike Oakes, May 18 2001

Keywords

Comments

Terms greater than 1000 may only be strong pseudoprimes. [Clarified by M. F. Hasler, Sep 16 2013]
No other terms less than 100000. - Robert Price, Mar 22 2012

Crossrefs

Cf. A000043, A057468, A059801-A059803, A062572-A062582, A188051, A062585-A062666.

Programs

A062592 Numbers k such that 26^k - 25^k is prime or a strong pseudoprime.

Original entry on oeis.org

3, 7, 97, 109, 401, 431
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

a(7) > 10^5. - Robert Price, Nov 10 2012

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062589, A214658, A214655, A062593-A062666.

Extensions

Edited by M. F. Hasler, Sep 21 2013

A121091 Smallest nexus prime of the form n^p - (n-1)^p, where p is an odd prime.

Original entry on oeis.org

7, 19, 37, 61, 4651, 127, 1273609, 2685817, 271, 331, 397, 6431804812640900941, 547, 631, 5613125740675652943160572913465695837595324940170321, 371281, 919
Offset: 2

Views

Author

Alexander Adamchuk, Aug 11 2006, revised Dec 01 2006, Feb 15 2007

Keywords

Comments

a(19) = 19^1607 - 18^1607, which is too large to include. It has 2055 decimal digits. See A062585(1) = 1607.
a(20)-a(21) = {723901, 8005616640331026125580781}. a(n) is currently known for all n up to n = 96. Corresponding smallest odd primes p such that (n+1)^p - n^p is prime are listed in A125713(n) = {3,3,3,3,5,3,7,7,3,3,3,17,3,3,43,5,3,10957,5,19,127,229,3,3,3,13,3,3,149,3,5,3,23,3,5,83,3,3,37,7,3,3,37,5,3,5,58543,...}. a(n+1) = A065013(n) for n = {4, 7, 10, 12, 13, 16, 17, 19, 22, 24, 25, 27, 28, 31, ...} = A047845(n) = (n-1)/2, where n runs through odd nonprimes (A014076), for n>1.

Crossrefs

Cf. A121620, A000043, A058765, A121616, A121618.
Cf. A125713 = Smallest odd prime p such that (n+1)^p - n^p is prime. Cf. A065913 = Smallest prime of form (n+1)^k - n^k. Cf. A058013 = Smallest prime p such that (n+1)^p - n^p is prime. Cf. A047845, A014076.
Cf. A062585 = numbers n such that k^n - (k-1)^n is prime, where k is 19. Cf. A000043, A057468, A059801, A059802, A062572-A062666.

Formula

a(n) = n^A125713(n) - (n-1)^A125713(n).

A214655 Numbers n such that 25^n - 24^n is prime or a strong pseudoprime.

Original entry on oeis.org

3, 5, 29, 54799
Offset: 1

Views

Author

Robert Price, Jul 24 2012

Keywords

Comments

All terms are prime.
No other terms less than 10^5. - Robert Price, Jul 24 2012

Crossrefs

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062589, A214658, A062592-A062666.

Programs

  • Mathematica
    Select[Range[10^5], PrimeQ[25^#-24^# ]&]

Extensions

Edited by M. F. Hasler, Sep 21 2013

A214658 Numbers n such that 24^n - 23^n is prime or a strong pseudoprime.

Original entry on oeis.org

2, 3, 31, 40519, 51061
Offset: 1

Views

Author

Robert Price, Jul 24 2012

Keywords

Comments

All terms are prime.
No other terms less than 10^5. - Robert Price, Jul 24 2012

Crossrefs

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062589, A214655, A062592-A062666.

Programs

  • Mathematica
    Select[Range[10^5], PrimeQ[24^#-23^# ]&]

A062578 Numbers k such that 12^k - 11^k is prime.

Original entry on oeis.org

2, 3, 7, 89, 101, 293, 4463, 70067
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

Terms greater than 1000 may correspond to unproven strong pseudoprimes.

Crossrefs

Cf. A000043, A057468, A059801, A059802, A062572-A062666.

Programs

Extensions

New term 70067 (found in 2006) from Jean-Louis Charton, Sep 02 2009
Edited by M. F. Hasler, Sep 16 2013

A062609 Numbers k such that 43^k - 42^k is prime or a strong pseudoprime.

Original entry on oeis.org

3, 13, 43, 211
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

a(5) > 10^5 - Robert Price, Dec 24 2012

Crossrefs

Cf. A000043, A057468, A059801-A059803, A062572-A062608, A215632, A062611-A062666.

Programs

  • PARI
    forprime(n=1, 9999, ispseudoprime(43^n-42^n) && print1(n", ")) \\ - M. F. Hasler, Sep 21 2013

Extensions

Edited by M. F. Hasler, Sep 21 2013

A062611 Numbers k such that 45^k - 44^k is prime or a strong pseudoprime.

Original entry on oeis.org

2, 5, 151, 223, 313, 1277, 8447
Offset: 1

Views

Author

Mike Oakes, May 18 2001, May 19 2001

Keywords

Comments

a(8) > 10^5. - Robert Price, Jan 02 2013

Crossrefs

Cf. A000043, A057468, A059801-A059803, A062572-A062609, A215632, A062612-A062666.

Programs

  • PARI
    forprime(n=1,9999,ispseudoprime(45^n-44^n)&print1(n",")) \\ - M. F. Hasler, Sep 21 2013

Extensions

Edited by M. F. Hasler, Sep 21 2013

A188051 Numbers k such that 18^k - 17^k is prime, or a strong pseudoprime.

Original entry on oeis.org

3, 13, 71, 14533, 26641, 48179
Offset: 1

Views

Author

Jean-Louis Charton, Mar 19 2011

Keywords

Comments

Terms < 10000 found by Mike Oakes.
Term 14533 found by Lelio R Paula in June 2008 corresponding to a probable prime with 18243 digits.
Terms 26641 and 48179 found by Jean-Louis Charton in December 2010 corresponding to probable primes with 33442 and 60478 digits.
a(7) > 10^5. - Robert Price, Nov 30 2012

Links

Crossrefs

Cf. A000043, A057468, A059801, A059802, A059803, A062572-A062583, A062585-A062666.

Programs

Extensions

Edited by M. F. Hasler, Sep 21 2013
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