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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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

A082869 3^n - 2^n is a semiprime.

Original entry on oeis.org

4, 7, 9, 13, 19, 23, 37, 71, 89, 97, 131, 167, 193, 227, 229, 257, 263, 269, 271
Offset: 1

Views

Author

Hugo Pfoertner, May 24 2003

Keywords

Comments

a(20) >= 653. - Max Alekseyev, Aug 26 2021

Examples

			a(1) = 4 because 3^4 - 2^4 = 5 * 13
a(2) = 7 because 3^7 - 2^7 = 29 * 71
a(3) = 9 because 3^9 - 2^9 = 1009 * 19
a(4) = 13 because 3^13 - 2^13 = 53 * 29927
a(5) = 19 because 3^19 - 2^19 = 1559 * 745181
a(6) = 23 because 3^23 - 2^23 = 47 * 2002867877
a(7) = 37 because 3^37 - 2^37 = 8891471 * 50642213021
a(8) = 71 because 3^71 - 2^71 = 67049419 * 111998979662707645844109121
a(9) = 89 because 3^89 - 2^89 = 4120081168939 * 706132008101135602203621405289
a(10) = 97 because 3^97 - 2^97 = 319128643 * 59813046375181769306016700165290169537
a(11) = 131 because 3^131 - 2^131 = 263 * 1210399177182288006201752262354382648158190136861552303421773
a(12) = 167 because 3^167 - 2^167 = 167884386911 * 284602839755962600307038183361142274453177384697761703968640951718869
a(13) = 193 because 3^193 - 2^193 = 773 * 157116815095122696291789672145814943987605497895096234870661710074857006307174092298131047
a(14) = 227 because 3^227 - 2^227 = 167360891302418779411 * 12102381564694515014432350438002672779054341887509579790377508212702751544613632122970969
a(15) = 229 because 3^229 - 2^229 = 271117470516046849 * 67237232094433305864393166477037402086197319313004074022941345112953840883539481643687544179
a(16) = 257 because 3^257 - 2^257 = 3650201327 * 114247220844165289049224917003868019618046824570124111266639206512722372880755761151052076786187552795911804402733
a(17) = 263 because 3^263 - 2^263 = 1789696394587605010251024191 * 169867630212703250249981022070263878299079238108093021871181171428200213741587995035055139427113909
a(18) = 269 because 3^269 - 2^269 = 3767 * 58833122596041019850277965408508940208380870952125838087379156948993498251689923575161076689330121444393974916753840891087813
a(19) = 271 because 3^271 - 2^271 = 2711 * 735750407736473144959046057264728365874119021724332398617327934122565857164514694088659506296666818455309890905079155116415309

Links

Crossrefs

Cf. A001047, A001358, A057468, A058765, A050244, A095027.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 30 2007

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

A125954 Least number k > 0 such that ((2n+1)^k - 2^k)/(2n-1) is prime.

Original entry on oeis.org

2, 2, 3, 2, 2, 3, 2, 2, 11, 2, 5, 11, 2, 2, 5, 71, 2, 3, 2, 2, 167, 2, 17, 3, 2, 197, 149, 2, 2, 3, 3, 2, 2267, 2, 2, 3, 3, 2, 29, 2, 2531, 167, 2, 7, 3, 3, 2, 61, 2, 2, 11, 2, 2, 157, 2, 5, 7, 7, 149, 3, 5, 2, 379, 2, 41, 3, 2, 2, 3, 79, 11, 3, 2, 2, 97, 3, 2, 3, 3, 2, 1321, 2, 17, 31, 2, 61
Offset: 0

Views

Author

Alexander Adamchuk, Feb 07 2007

Keywords

Comments

All terms are primes.
a(n) = 2 for n = {1,2,4,5,7,8,10,13,14,17,19,20,22,...} = A067076 Numbers n such that 2n+3 is a prime.
a(34),...,a(40) = {2,2,3,3,2,29,2}.
a(42),...,a(80) = {167,2,7,3,3,2,61,2,2,11,2,2,157,2,5,7,7,149,3,5,2,379,2,41,3,2,2,3,79,11,3,2,2,97,3,2,3,3,2}.
a(82),...,a(90) = {2,17,31,2,61,7,2,2,5}.
a(93),...,a(95) = {383,2,2}.
a(97),...,a(100) = {2,2,5,7}.
a(102),...,a(124) = {13,11,2,5,5,17,3,103,2,19,2,2,3,2,31,37,2,2,3,3,7,3,2}.
a(127),...,a(131) = {2,61,31,2,157}.
a(133),...,a(142) = {2,2,7,3,2,13,2,2,7,3}.
a(144),...,a(146) = {173,2,11}.
a(148),...,a(150) = {3,17,107}.
a(n) is currently unknown for n = {33,41,81,91,92,96,101,125,126,132,143,147,...}.

Crossrefs

Cf. A067076.
Cf. A000043 = Primes p such that 2^p - 1 is prime.
Cf. A001348 = Mersenne numbers: 2^p - 1, where p is prime.
Cf. A057468 = numbers n such that 3^n - 2^n is prime.
Cf. A125958 = Least number k > 0 such that (2^k + (2n-1)^k)/(2n+1) is prime.

Programs

  • Mathematica
    Do[k = 1; While[ !PrimeQ[((2n+1)^k - 2^k)/(2n-1)], k++ ]; Print[k], {n, 100}] (* Ryan Propper, Mar 29 2007 *)
lnk[n_]:=Module[{k=1},While[!PrimeQ[((2n+1)^k-2^k)/(2n-1)],k++];k]; Array[ lnk,90] (* Harvey P. Dale, May 19 2012 *)

Extensions

More terms from Ryan Propper, Mar 29 2007
Previous Showing 31-40 of 123 results. Next

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