A057468 -id:A057468 - cp's OEIS frontend

A058765 Primes of the form 3^k - 2^k.

5, 19, 211, 129009091, 68629840493971, 617671248800299, 19383245658672820642055731, 14130386091162273752461387579, 1546132562196033990574082188840405015112916155251

Offset: 1

N. J. A. Sloane, Jan 02 2001

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..12

Cf. A001047 (3^n-2^n) and A057468 (k such that 3^k-2^k is prime).

Filtered(List([1..200],n->3^n - 2^n),IsPrime); # Muniru A Asiru, Mar 04 2018

[a: n in [0..300] | IsPrime(a) where a is  3^n - 2^n]; // Vincenzo Librandi, Dec 08 2011

select(isprime, [seq(3^n - 2^n, n=0..200)]); # Muniru A Asiru, Mar 04 2018

Select[Table[3^n-2^n, {n,0,2200}], PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)

lista(nn) = for(k=1, nn, if(isprime(p=3^k-2^k), print1(p", "))) \\ Altug Alkan, Mar 04 2018

a(n) = A001047(A057468(n)).

A280149 Numbers k such that 3^k - 2^k is not squarefree.

Original entry on oeis.org

10, 11, 20, 22, 30, 33, 40, 42, 44, 50, 52, 55, 57, 60, 66, 70, 77, 80, 84, 88, 90, 99, 100, 104, 110, 114, 120, 121, 126, 130, 132, 140, 143, 150, 154, 156, 160, 165, 168, 170, 171, 176, 180, 187, 190, 198, 200, 203, 208, 209, 210, 220, 228, 230, 231, 240, 242, 250, 252, 253, 260, 264, 270, 272, 275, 280, 285

Offset: 1

Juri-Stepan Gerasimov, Dec 27 2016

nonn

Primitive members (not multiples of earlier terms) are 10, 11, 42, 52, 57, 203, 272, 497, .... - Juri-Stepan Gerasimov and Charles R Greathouse IV, Dec 27 2016
From Robert Israel, Dec 27 2016: (Start)
Numbers divisible by the order of 3/2 mod p^2 for some prime p > 3.
Includes numbers divisible by p^2-p for some prime p > 3.
If k is a member, then so are all multiples of k. (End)

			10 is in this sequence because 3^10 - 2^10 = 58025 = 5^2*11*211.

Charles R Greathouse IV and Amiram Eldar, Table of n, a(n) for n = 1..134 (terms 1..127 from Charles R Greathouse IV)

Cf. A001047, A005117, A013929, A049094, A057468, A082869, A282688, A282689.

[n: n in [1..156] | not IsSquarefree(3^n-2^n)];

Select[Range@ 120, ! SquareFreeQ[3^# - 2^#] &] (* Michael De Vlieger, Dec 27 2016 *)

is(n)=issquarefree(3^n-2^n)==0 \\ Charles R Greathouse IV, Dec 27 2016

More terms from Charles R Greathouse IV, Dec 27 2016

A062577 Numbers k such that 11^k - 10^k is prime.

Original entry on oeis.org

3, 5, 19, 311, 317, 1129, 4253, 7699, 18199, 35153, 206081

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

Terms greater than 1000 may correspond to unproven strong pseudoprimes.

Top probable primes of the form 11^p-10^p

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

is(n)=ispseudoprime(11^n-10^n) \\ Charles R Greathouse IV, Feb 17 2017

Two more terms 18199 and 35153 from Jean-Louis Charton, Sep 02 2009
New term 206081 found by Jean-Louis Charton in October 2011
Edited by M. F. Hasler, Sep 16 2013

A062576 Numbers k such that 10^k - 9^k is prime.

Original entry on oeis.org

2, 3, 7, 11, 19, 29, 401, 709, 2531, 15787, 66949, 282493

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

Terms > 1000 are often only strong pseudoprimes.

All terms are prime. - Alexander Adamchuk, Apr 27 2008

			10^2 - 9^2 = 100 - 81 = 19, which is prime, hence 2 is in the sequence.
10^3 - 9^3 = 1000 - 729 = 271, which is prime, hence 3 is in the sequence.
10^4 - 9^4 = 10000 - 6561 = 3439 = 19 * 181, which is not prime, hence 4 is not in the sequence.

Henri & Renaud Lifchitz, PRP Records.

Cf. A000043, A057468, A059801, A059802, A059803 (9^n-8^n is prime), A062572-A062666.

Cf. A016189 = 10^n - 9^n, and A199819 (primes of this form).

Select[Range[1000], PrimeQ[10^# - 9^#] &] (* Alonso del Arte, Sep 06 2013 *)

is(n)=ispseudoprime(10^n-9^n) \\ Charles R Greathouse IV, Feb 20 2017

Three more terms 15787, 66949 and 282493 found by Jean-Louis Charton in 2004 and 2007

A125713 Smallest odd prime p such that (n+1)^p - n^p is prime.

Original entry on oeis.org

3, 3, 3, 3, 5, 3, 7, 7, 3, 3, 3, 17, 3, 3, 43, 5, 3, 1607, 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, 3, 3, 7, 29, 3, 479, 5, 3, 19, 5, 3, 4663, 54517, 17, 3, 3, 5, 7, 3, 3, 17, 11, 47, 61, 19, 23, 3, 5, 19, 7, 5, 7, 3, 3

Offset: 1

Alexander Adamchuk, Dec 01 2006, Feb 15 2007

Corresponding smallest primes of the form (n+1)^p - n^p, where p = a(n) is an odd prime, are listed in A121091(n+1) = {7, 19, 37, 61, 4651, 127, 1273609, 2685817, 271, 331, 397, 6431804812640900941, 547, 631, ...}. a(n) = A058013(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. a(97) = 7. a(99)..a(112) = {5, 43, 5, 13, 7, 5, 3, 6529, 59, 3, 5, 5, 113, 5}. a(114) = 139. a(117)..a(129) = {7, 13, 3, 5, 5, 7, 3, 5167, 3, 41, 59, 3, 3}. a(131) = 101. a(n) is currently unknown for n = {113, 115, 116, 130, 132, ...}.
a(96) = 1307, a(98) = 709.
a(137) is probably 196873 from a prime of this form discovered by Jean-Louis Charton in December 2009 and reported to Henri Lifchitz's PRP Top. - Robert Price, Feb 17 2012
a(138) through a(150) are 113, >32401, 3, 7, 3, 8839, 5, 7, 13, 3, 5, 271, 13. - Robert Price, Feb 17 2012
a(137) = 196873 confirmed by Fischer link; a(139) > 260000. - Ray Chandler, Feb 26 2017

Robert Price and Ray Chandler, Table of n, a(n) for n = 1..138 (first 136 terms from Robert Price)
Richard Fischer, Generalized primes of the form (B+1)^N - B^N.

Cf. A058013 (smallest prime p such that (n+1)^p - n^p is prime).
Cf. A065913 (smallest prime of form (n+1)^k - n^k).
Cf. A121091 (smallest nexus prime of the form n^p - (n-1)^p, where p is odd 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.

A216181 Numbers n such that (11^n - 4^n)/7 is prime.

Original entry on oeis.org

3, 5, 11, 17, 71, 89, 827, 22307, 45893, 63521

Offset: 1

Robert Price, Mar 11 2013

All terms are prime.

Next term > 10^5.

Cf. A004063, A028491, A057468, A059801, A121877, A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032, A210506.

Select[Prime[Range[1, 100000]], PrimeQ[(11^# - 4^#)/7]&]

is(n)=ispseudoprime((11^n-4^n)/7) \\ Charles R Greathouse IV, Feb 20 2017

A062573 Numbers k such that 7^k - 6^k is prime.

Original entry on oeis.org

2, 3, 7, 29, 41, 67, 1327, 1399, 2027, 69371, 86689, 355039

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

Terms greater than 1000 often correspond only to strong probable primes.

			7^2 - 6^2 = 49 - 36 = 13, which is prime, so 2 is in the sequence.
7^3 - 6^3 = 343 - 216 = 127, which is prime, so 3 is in the sequence.

Henri & Renaud Lifchitz, Top probable primes of the form 7^p-6^p

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

Select[Range[100], PrimeQ[7^# - 6^#] &] (* Alonso del Arte, Sep 04 2013 *)

is(n)=ispseudoprime(7^n-6^n) \\ Charles R Greathouse IV, Feb 20 2017

Two more terms (69371 and 86689) found by Predrag Minovic in 2004 corresponding to probable primes with 58626 and 73261 digits. - Jean-Louis Charton, Oct 06 2010

New term 355039 found by Jean-Louis Charton in May 2011 corresponding to a probable prime with 300043 digits.

A062574 Numbers k such that 8^k - 7^k is prime or a strong pseudoprime.

Original entry on oeis.org

7, 11, 17, 29, 31, 79, 113, 131, 139, 4357, 44029, 76213, 83663, 173687, 336419, 615997

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

All terms are prime. - Alexander Adamchuk, Apr 27 2008

Henri & Renaud Lifchitz, PRP Records.

Cf. A000043, A057468, A059801, A059802, A059803 (9^n-8^n is prime), A062572-A062666.

Cf. A016177 = 8^n - 7^n.

Select[Range[200], PrimeQ[8^# - 7^#] &] (* Vladimir Joseph Stephan Orlovsky, Feb 22 2012 *)

is(n)=ispseudoprime(8^n-7^n) \\ Charles R Greathouse IV, Sep 04 2013

Two more terms 44029 and 76213 found by Ananda Tallur & Jean-Louis Charton in 2003.
Three more terms 83663, 173687 and 336419 found by Jean-Louis Charton in 2004 and 2008
New term 615997 found by Jean-Louis Charton corresponding to a probable prime with 556301 digits. Jean-Louis Charton, Sep 02 2009

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

Original entry on oeis.org

2, 1607, 1873, 10957

Offset: 1

Mike Oakes, May 18 2001, May 19 2001

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

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

is(n)=ispseudoprime(19^n-18^n) \\ Charles R Greathouse IV, Feb 20 2017

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

A283653 Numbers k such that 3^k + (-2)^k is prime.

Original entry on oeis.org

0, 2, 3, 4, 5, 17, 29, 31, 53, 59, 101, 277, 647, 1061, 2381, 2833, 3613, 3853, 3929, 5297, 7417, 90217, 122219, 173191, 256199, 336353, 485977, 591827, 1059503

Offset: 1

Juri-Stepan Gerasimov, Mar 12 2017

Numbers j such that both 3^j + (-2)^j and 3^j + (-4)^j are primes: 0, 3, 4, 17, 59, ...
See Michael Somos comment in A082101.
Probably this is just A057468 with 0,2,4 added, because we already know that if another even number belong to this sequence it must be greater than log_3(10^16000000) = about 3.3*10^7. This is because 3^n+2^n can be a prime with n>0 only if n is a power of 2. - Giovanni Resta, Mar 12 2017

			4 is in this sequence because 3^4 + (-2)^4 = 97 is prime.

Cf. A174326. Subsequence of A087451. Supersequence of A057468.

Cf. A082101.

[n: n in [0..1000] | IsPrime(3^n+(-2)^n)];

Select[Range[0, 10000], PrimeQ[3^# + (-2)^#] &] (* G. C. Greubel, Jul 29 2018 *)

is(n)=isprime(3^n+(-2)^n) \\ Charles R Greathouse IV, Mar 16 2017

cp's OEIS Frontend

A058765 Primes of the form 3^k - 2^k.

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A280149 Numbers k such that 3^k - 2^k is not squarefree.

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A062577 Numbers k such that 11^k - 10^k is prime.

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A062576 Numbers k such that 10^k - 9^k is prime.

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A125713 Smallest odd prime p such that (n+1)^p - n^p is prime.

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A216181 Numbers n such that (11^n - 4^n)/7 is prime.

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A062573 Numbers k such that 7^k - 6^k is prime.

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A062574 Numbers k such that 8^k - 7^k is prime or a strong pseudoprime.

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