A090669 -id:A090669 - cp's OEIS frontend

A217131 Numbers n such that 7^n - 8 is prime.

2, 4, 8, 10, 50, 106, 182, 293, 964, 1108, 1654, 1756, 4601, 8870, 15100, 17446, 22742, 34570, 50150, 95276

Offset: 1

Vincenzo Librandi, Oct 01 2012

nonn

a(21) > 10^5. - Robert Price, Jan 23 2014

Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Select[Range[1, 5000], PrimeQ[7^#  - 8] &]

for(n=1, 5*10^3, if(isprime(7^n-8), print1(n, ", ")))

a(14)-a(20) from Robert Price, Jan 23 2014

A152213 Numbers n such that 7^n + 12 is prime.

Original entry on oeis.org

0, 1, 2, 9, 66, 164, 221, 224, 2058, 3224, 12284, 13457, 22277, 22761, 83381

Offset: 1

Huseyin Azoguz (huseyin(AT)mmnetz.de), Nov 29 2008

a(16) > 10^5. - Robert Price, Jan 24 2014

Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Select[Range[0,84000],PrimeQ[7^#+12]&] (* Harvey P. Dale, Dec 03 2017 *)

is(n)=ispseudoprime(7^n+12) \\ Charles R Greathouse IV, Feb 17 2017

a(11)-a(15) from Robert Price, Jan 24 2014

A217132 Numbers n such that 7^n + 10 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 11, 26, 29, 41, 53, 55, 84, 86, 144, 179, 229, 238, 414, 616, 1158, 4111, 5577, 13237, 15244, 48578, 66074

Offset: 1

Vincenzo Librandi, Oct 01 2012

nonn

a(29) > 10^5. - Robert Price, Jan 24 2014

Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Select[Range[0, 3000], PrimeQ[7^# + 10] &]

for(n=1, 3*10^3, if(isprime(7^n+10), print1(n", ")))

a(23)-a(28) from Robert Price, Jan 24 2014

A236371 Numbers n such that 7^n - 12 is prime.

Original entry on oeis.org

2, 3, 4, 12, 27, 28, 34, 36, 147, 179, 242, 276, 278, 466, 735, 2371, 4548, 5606, 10324, 82899

Offset: 1

Robert Price, Jan 23 2014

nonn

a(21) > 10^5.

Cf. A236371, A217131, A191469, A090669, A096305, A217130, A217132, A152213.

Select[Range[1, 100000], PrimeQ[7^# - 12] &]

for(n=1, 5*10^5, if(isprime(7^n-12), print1(n, ", ")))

A130652 a(n) = 11^n - 2.

Original entry on oeis.org

9, 119, 1329, 14639, 161049, 1771559, 19487169, 214358879, 2357947689, 25937424599, 285311670609, 3138428376719, 34522712143929, 379749833583239, 4177248169415649, 45949729863572159, 505447028499293769, 5559917313492231479, 61159090448414546289, 672749994932560009199

Offset: 1

Alexander Adamchuk, Jun 20 2007

There are only two known primes in a(n): a(4) = 14639 and a(6) = 1771559 (see A128472 = smallest prime of the form (2n-1)^k - 2 for k > (2n-1), or 0 if no such number exists). 3 divides a(2k-1). 7 divides a(3k-1). 13 divides a(12k-5). 17 divides a(16k-14).
Final digit of a(n) is 9.
Final two digits of a(n) are periodic with period 10: a(n) mod 100 = {09, 19, 29, 39, 49, 59, 69, 79, 89, 99}.
Final three digits of a(n) are periodic with period 50: a(n) mod 1000 = {009, 119, 329, 639, 049, 559, 169, 879, 689, 599, 609, 719, 929, 239, 649, 159, 769, 479, 289, 199, 209, 319, 529, 839, 249, 759, 369, 079, 889, 799, 809, 919, 129, 439, 849, 359, 969, 679, 489, 399, 409, 519, 729, 039, 449, 959, 569, 279, 089, 999}.

Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (12,-11).

Cf. A001020, A024127, A034524. Cf. A104096 = Largest prime <= 11^n. Cf. A084714 = smallest prime of the form (2n-1)^k - 2, or 0 if no such number exists. Cf. A128472 = smallest prime of the form (2n-1)^k - 2 for k>(2n-1), or 0 if no such number exists. Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

[11^n - 2: n in [1..50]]; // Vincenzo Librandi, Jun 08 2011

LinearRecurrence[{12, -11},{9, 119},17] (* Ray Chandler, Aug 26 2015 *)

a(n) = 11*a(n-1) + 20; a(1)=9. - Vincenzo Librandi, Jun 08 2011
From Elmo R. Oliveira, Jun 16 2025: (Start)
G.f.: x*(11*x+9)/((11*x-1)*(x-1)).
E.g.f.: 1 + exp(x)*(exp(10*x) - 2).
a(n) = 12*a(n-1) - 11*a(n-2) for n > 2. (End)

A133858 Primes of the form 11^k - 2.

Original entry on oeis.org

14639, 1771559

Offset: 1

Alexander Adamchuk, Sep 27 2007

Last digit of all terms is 9.

The nest term (11^22420-2) is too large to be displayed; see A133982 for the corresponding k. - Joerg Arndt, Nov 28 2020

			a(1) = 11^4 - 2 = 14639,
a(2) = 11^6 - 2 = 1771559.

Cf. A104096 (largest prime <= 11^n), A130652, A128472, A084714 (smallest prime of the form (2n-1)^k - 2).

Cf. A014224, A109080, A090669, A128455, A133982, A128457, A128458, A128459, A128460, A128461.

A155899 Square matrix T(m,n)=1 if (2m+1)^(2n-1)-2 is prime, 0 otherwise; read by antidiagonals.

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0

Offset: 1

M. F. Hasler, Feb 01 2009

In some sense the "minimal" possible generalization of the pattern of Mersenne primes (cf. A000043) is to consider powers of odd numbers minus 2. Here only odd powers are considered.

Cf. A084714, A128472, A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.

T = matrix( 19,19,m,n, isprime((2*m+1)^(2*n-1)-2)) ;
A155899 = concat( vector( vecmin( matsize(T)), i, vector( i, j, T[j,i-j+1])))

A093612 Primes of form 7^n-2.

Original entry on oeis.org

5, 47, 2399, 823541, 5764799, 13841287199, 4747561509941, 459986536544739960976799, 157775382034845806615042741, 97327453648743672783790144527749033795901408624680013074608083129650399

Offset: 1

Arnaud Vernier, May 23 2004

nonn

The exponents n are listed in A090669, cf. formula. [From M. F. Hasler, Nov 26 2009]

The next term (a(11)) has 83 digits. - Harvey P. Dale, Nov 14 2014

Cf. A014232.

Select[7^Range[90]-2,PrimeQ] (* Harvey P. Dale, Nov 14 2014 *)

a(n)=7^A090669(n)-2. [From M. F. Hasler, Nov 26 2009]

Terms beyond a(6) from M. F. Hasler, Nov 26 2009

A133856 Least number k > (2n-1) such that (2n-1)^k - 2 is prime, or 0 if no such number exists.

Original entry on oeis.org

0, 4, 14, 8, 11, 22420, 78, 17, 24, 20, 25, 24, 63, 30, 42, 69, 128, 50, 119, 204, 2816, 76, 52, 288, 64, 66, 184, 153, 67, 268, 78, 210, 438, 295, 96, 74, 136, 128, 2900, 1898, 130, 92, 381, 106, 18626, 97, 98, 1650, 747, 109, 214, 113, 312, 354, 1702, 560, 2798, 123, 171, 554, 11210, 834, 208, 990, 9271

Offset: 1

Alexander Adamchuk, Oct 01 2007

nonn

a(66) > 40000. - Robert Price, Mar 02 2015

Henri Lifchitz & Renaud Lifchitz: PRP Records. Probable Primes Top 10000.

Cf. A128472 (smallest prime of the form (2n-1)^k - 2 for k > (2n-1), or 0 if no such number exists).
Cf. A084714 (smallest prime of the form (2n-1)^k - 2, or 0 if no such number exists).
Cf. A014224, A109080, A090669, A128455, A128457, A128458, A128459, A128460, A128461.
Cf. A133858, A133982.

A128472(n) = (2n-1)^a(n) - 2 for n > 1.

a(6) = 22420 was found by Rick L. Shepherd, Sep 29 2009
a(21)-a(44) from Max Alekseyev, Oct 04 2007
a(45)-a(65) from Robert Price, Mar 02 2015

A147782 Primes p such that 7^p - 2 is prime.

Original entry on oeis.org

2, 7, 31, 859

Offset: 1

Cino Hilliard, Nov 12 2008

m=7 in the PARI script. 13 is the next base prime for which this condition holds. In fact, the base prime q in q^p-2 is prime must be of the form 6n+1.
This follows from the fact that if q = 6n-1, the binomial q^p = (6n-1)^p = 6h-1 for some h and q^p-2 = 6h-1-2 is divisible by 3 and thus not prime.
a(5) > 90263. - J.W.L. (Jan) Eerland, Dec 11 2022
a(5) > 274120 using A090669. - Michael S. Branicky, Jul 07 2024

Cf. A000040, A090669.

Select[Prime[Range[150]],PrimeQ[7^#-2]&] (* Harvey P. Dale, Feb 20 2013 *)

g(n,m)=forprime(p=2,n,y=m^p-2;if(ispseudoprime(y),print1(p",")))

A000040 INTERSECT A090669. - R. J. Mathar, Jan 22 2009

Offset corrected by Mohammed Yaseen, Jul 20 2023

cp's OEIS Frontend

A217131 Numbers n such that 7^n - 8 is prime.

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A152213 Numbers n such that 7^n + 12 is prime.

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A217132 Numbers n such that 7^n + 10 is prime.

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A236371 Numbers n such that 7^n - 12 is prime.

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A130652 a(n) = 11^n - 2.

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A133858 Primes of the form 11^k - 2.

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A155899 Square matrix T(m,n)=1 if (2m+1)^(2n-1)-2 is prime, 0 otherwise; read by antidiagonals.

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PARI

A093612 Primes of form 7^n-2.

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A133856 Least number k > (2n-1) such that (2n-1)^k - 2 is prime, or 0 if no such number exists.

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