A104096 -id:A104096 - cp's OEIS frontend

A104089 Largest prime <= 4^n.

3, 13, 61, 251, 1021, 4093, 16381, 65521, 262139, 1048573, 4194301, 16777213, 67108859, 268435399, 1073741789, 4294967291, 17179869143, 68719476731, 274877906899, 1099511627689, 4398046511093, 17592186044399, 70368744177643

Offset: 1

Cino Hilliard, Mar 03 2005

Cf. A014234, A104082, A104088, A104090-A104094, A003618, A104096.

Cf. A000040, A000302, A007917.

NextPrime[4^Range[30], -1] (* Paolo Xausa, Oct 28 2024 *)

g(n,b) = for(x=0,n,print1(precprime(b^x)","))

a(n) = A007917(A000302(n)). - Paolo Xausa, Oct 28 2024

A104090 Largest prime <= 5^n.

Original entry on oeis.org

5, 23, 113, 619, 3121, 15619, 78121, 390581, 1953109, 9765619, 48828113, 244140613, 1220703073, 6103515623, 30517578121, 152587890563, 762939453109, 3814697265523, 19073486328109, 95367431640599, 476837158203071, 2384185791015571, 11920928955078089

Offset: 1

Cino Hilliard, Mar 03 2005

Cf. A014234, A054321, A104088, A104089, A104091-A104094, A003618, A104096.

Cf. A000040, A000351, A007917.

NextPrime[5^Range[30] + 1, -1] (* Paolo Xausa, Oct 29 2024 *)

g(n,b) = for(x=0,n,print1(precprime(b^x)","))

a(n) = A007917(A000351(n)). - Paolo Xausa, Oct 29 2024

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.

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A104089 Largest prime <= 4^n.

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A104090 Largest prime <= 5^n.

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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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