A125957 -id:A125957 - cp's OEIS frontend

A127931 Numbers k such that 13 divides 11*k + 2^k.

1, 2, 6, 9, 23, 29, 70, 72, 103, 112, 128, 147, 157, 158, 162, 165, 179, 185, 226, 228, 259, 268, 284, 303, 313, 314, 318, 321, 335, 341, 382, 384, 415, 424, 440, 459, 469, 470, 474, 477, 491, 497, 538, 540, 571, 580, 596, 615, 625, 626, 630, 633, 647, 653

Offset: 1

Zak Seidov, Feb 07 2007, Feb 09 2007

Sequence is infinite: starting with the 13th term, a(13)=157, a(i)=a(i-12)+156. In general, for p and p-2 both prime, starting with p-th term, a(i-(p-1))+p(p-1). This particular sequence corresponds to the case p=13.

First differences have period 12. - Charles R Greathouse IV, Oct 11 2013

G. C. Greubel, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Cf. A125957.

Select[Range[700],Divisible[11#+2^#,13]&] (* or *) LinearRecurrence[ {1,0,0,0,0,0,0,0,0,0,0,1,-1},{1,2,6,9,23,29,70,72,103,112,128,147,157}, 60] (* Harvey P. Dale, Sep 03 2016 *)

isok(n) = ((11*n + 2^n) % 13) == 0; \\ Michel Marcus, Oct 11 2013

a(n) = a(n-1) + a(n-12) - a(n-13). - Wesley Ivan Hurt, Feb 22 2022

A225191 Numbers n such that (15^n + 2^n)/17 is prime.

Original entry on oeis.org

3, 67, 199, 479, 563, 2243, 2579, 6599, 7951, 10099, 10909, 13759

Offset: 1

Robert Price, May 07 2013

All terms are odd primes.

a(13) > 10^5.

Cf. A057181, A125956, A125957, A222265.

Select[Prime[Range[1, 100000]], PrimeQ[(15^# + 2^#)/17]&]

forprime(p=3,10^6, if(ispseudoprime((15^p + 2^p)/17), print1(p,", ") ) ); \\ Joerg Arndt, Jul 29 2013

Removed incorrect first term of "2".

A222265 Numbers n such that (13^n + 2^n)/15 is prime.

Original entry on oeis.org

7, 31, 103, 223, 503, 1171, 1973, 4111, 4729

Offset: 1

Robert Price, May 05 2013

All terms are prime.

a(10) > 10^5.

Cf. A125956, A125957, A057159, A128071, A213176.

Select[Prime[Range[1, 100000]], PrimeQ[(13^# + 2^#)/15]&]

forprime(p=3,10^6, if(ispseudoprime((13^p + 2^p)/15), print1(p,", ") ) ); \\ Joerg Arndt, Jul 29 2013

Removed incorrect first term of "2".

A224507 Numbers n such that (17^n + 2^n)/19 is prime.

Original entry on oeis.org

5, 7, 113, 193, 211, 701, 797, 907, 4153

Offset: 1

Robert Price, Jul 20 2013

All terms are prime.

a(10) > 10^5.

Cf. A057183, A125957, A222265, A225191, A227046.

Select[Prime[Range[1, 100000]], PrimeQ[(17^# + 2^#)/19]&]

is(n)=ispseudoprime((17^n+2^n)/19) \\ Charles R Greathouse IV, Jun 06 2017

A338525 Numbers k such that (11^k + 6^k)/17 is prime.

Original entry on oeis.org

5, 7, 107, 383, 17359, 21929, 26393

Offset: 1

Tim Johannes Ohrtmann, Nov 01 2020

All terms are prime.

The corresponding primes are 9931, 1162771, ...

Wikipedia, Mersenne prime

Cf. A057177, A125957, A128070, A224501, A128340.

[n: n in [1..10000] |IsPrime((11^n + 6^n)/17)]

Select[Range[1, 10000], PrimeQ[(11^# + 6^#)/17] &]

for(n=1, 10000, if(isprime((11^n + 6^n)/17), print1(n, ", ")))

cp's OEIS Frontend

A127931 Numbers k such that 13 divides 11*k + 2^k.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A225191 Numbers n such that (15^n + 2^n)/17 is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

Extensions

A222265 Numbers n such that (13^n + 2^n)/15 is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

Extensions

A224507 Numbers n such that (17^n + 2^n)/19 is prime.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

PARI

A338525 Numbers k such that (11^k + 6^k)/17 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI