A191469 -id:A191469 - cp's OEIS frontend

A090669 Numbers k such that 7^k - 2 is a prime.

1, 2, 4, 7, 8, 12, 15, 28, 31, 84, 98, 128, 238, 302, 859, 1508, 1586, 2091, 2796, 2888, 3924, 4815, 5636, 6596, 7090, 20176, 22176, 56386, 84050, 115515, 245608, 259710, 274120

Offset: 1

Herman H. Rosenfeld (herm3(AT)pacbell.net), Dec 16 2003

			7^12 - 2 = 13841287199 a prime number.

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

Do[ If[ PrimeQ[7^n - 2], Print[n]], {n, 1, 2000}] (* Robert G. Wilson v, Dec 22 2003 *)

is(n)=isprime(7^n - 2) \\ Charles R Greathouse IV, Apr 28 2015

Corrected and extended by Robert G. Wilson v and Ray Chandler, Dec 22 2003
Three more terms from Ryan Propper, Dec 07 2008
a(28)-a(30) from Robert Price, Jan 24 2014
a(31)-a(32) from Paul Bourdelais, Jan 29 2021
a(33) from Paul Bourdelais, Aug 02 2023

A096305 Numbers k such that 7^k + 4 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 9, 14, 23, 129, 198, 235, 275, 630, 870, 1033, 1290, 3293, 3458, 11466, 13885, 25893, 32186, 33139, 58125, 78929, 97197, 121933, 128422, 442674

Offset: 1

Herman H. Rosenfeld (herm3(AT)pacbell.net), Jun 26 2004

			7^14 + 4 = 678223072853 is a prime number.

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

Do[If[PrimeQ[7^n+4], Print[n]], {n, 1, 1000}]

for(n=0, 10^5, if(ispseudoprime(7^n+4), print1(n, ", "))) \\  Felix Fröhlich, Jun 04 2014

More terms (probable primes) from Rick L. Shepherd, Jun 29 2004
7 more terms from Jason Earls, Feb 16 2008
a(25)-a(27) from Robert Price, Jan 24 2014
a(28)-a(29) from Lelio R. Paula, Nov 2014
a(30) from Paul Bourdelais, Feb 11 2021

A217130 Numbers n such that 7^n + 6 is prime.

Original entry on oeis.org

0, 1, 3, 16, 36, 244, 315, 2577, 9500, 17596, 25551, 32193, 32835, 36504, 75136

Offset: 1

Vincenzo Librandi, Oct 01 2012

nonn

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

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

/* The code produces the sequence up to 315: */ [n: n in [0..2000] | IsPrime(7^n+6)];

Select[Range[0, 5000], PrimeQ[7^# + 6] &]

for(n=1, 5000, if(isprime(7^n+6), print1(n", ")))

a(9)-a(15) from Robert Price, Jan 24 2014

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

Original entry on oeis.org

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, ", ")))

A028499 6-hyperperfect numbers: n = 6*(sigma(n) - n - 1) + 1.

Original entry on oeis.org

301, 16513, 60110701, 1977225901, 2733834545701, 232630479398401, 336823287227717101

Offset: 1

Jud McCranie

(7^k-6)*7^(k-1) is a term for all k in A191469. - Max Alekseyev, Nov 17 2019

Antal Bege, Kinga Fogarasi, Generalized perfect numbers, Acta Univ. Sapientiae, Math., 1 (2009), 73-82.
Judson S. McCranie, A Study of Hyperperfect Numbers, Journal of Integer Sequences, Vol. 3 (2000), Article 00.1.3.
Eric Weisstein's World of Mathematics, Hyperperfect Number

Cf. A000396, A007593, A028500, A028501, A028502, A034916, A220290.

isok(n) = 6*(sigma(n) - n - 1) + 1 == n; \\ Michel Marcus, Nov 18 2019

a(5) from Donovan Johnson, Nov 20 2012
a(6) from Donovan Johnson confirmed by Max Alekseyev, Nov 17 2019
a(7) from Giovanni Resta confirmed by Max Alekseyev, May 23 2025

A291861 Prime numbers of the form 7^k - 6.

Original entry on oeis.org

43, 337, 117643, 40353601, 558545864083284001, 1341068619663964900801, 7730993719707444524137094401, 256923577521058878088611477224235621321601, 4318114567396436564035293097707728087552248843

Offset: 1

Robert Price, Sep 04 2017

nonn

Robert Price, Table of n, a(n) for n = 1..10
F. Firoozbakht and M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.
Henri & Renaud Lifchitz, PRP Records
OpenPFGW Project, Primality Tester

Cf. A191469.

Select[Table[7^k - 6, {k, 1, 100}], PrimeQ[#] &]

A305531 Smallest k >= 1 such that (n-1)*n^k + 1 is prime.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 3, 10, 3, 1, 2, 1, 1, 4, 1, 29, 14, 1, 1, 14, 2, 1, 2, 4, 1, 2, 4, 5, 12, 2, 1, 2, 2, 9, 16, 1, 2, 80, 1, 2, 4, 2, 3, 16, 2, 2, 2, 1, 15, 960, 15, 1, 4, 3, 1, 14, 1, 6, 20, 1, 3, 946, 6, 1, 18, 10, 1, 4, 1, 5, 42, 4, 1, 828, 1, 1, 2, 1, 12, 2, 6, 4, 30, 3, 3022, 2, 1, 1

Offset: 2

Eric Chen, Jun 04 2018

nonn

a(prime(j)) + 1 = A087139(j).
a(123) > 10^5, a(342) > 10^5, see the Barnes link for the Sierpinski base-123 and base-342 problems.
a(251) > 73000, see A087139.

Eric Chen, Table of n, a(n) for n = 2..122
Gary Barnes, Sierpinski conjectures and proofs
Eric Chen, Table n, a(n) for n = 2..360 status

For the numbers k such that these forms are prime:
a1(b): numbers k such that (b-1)*b^k-1 is prime
a2(b): numbers k such that (b-1)*b^k+1 is prime
a3(b): numbers k such that (b+1)*b^k-1 is prime
a4(b): numbers k such that (b+1)*b^k+1 is prime (no such k exists when b == 1 (mod 3))
a5(b): numbers k such that b^k-(b-1) is prime
a6(b): numbers k such that b^k+(b-1) is prime
a7(b): numbers k such that b^k-(b+1) is prime
a8(b): numbers k such that b^k+(b+1) is prime (no such k exists when b == 1 (mod 3)).
Using "-------" if there is currently no OEIS sequence and "xxxxxxx" if no such k exists (this occurs only for a4(b) and a8(b) for b == 1 (mod 3)):
.
   b   a1(b)   a2(b)   a3(b)   a4(b)   a5(b)   a6(b)   a7(b)   a8(b)
--------------------------------------------------------------------
   2 A000043 ------- A002235 A002253 A000043 ------- A050414 A057732
   3 A003307 A003306 A005540 A005537 A014224 A051783 A058959 A058958
   4 A272057 ------- ------- xxxxxxx A059266 A089437 A217348 xxxxxxx
   5 A046865 A204322 A257790 A143279 A059613 A124621 A165701 A089142
   6 A079906 A247260 ------- ------- A059614 A145106 A217352 A217351
   7 A046866 A245241 ------- xxxxxxx A191469 A217130 A217131 xxxxxxx
   8 A268061 A269544 ------- ------- A217380 A217381 A217383 A217382
   9 A268356 A056799 ------- ------- A177093 A217385 A217493 A217492
  10 A056725 A056797 A111391 xxxxxxx A095714 A088275 A092767 xxxxxxx
  11 A046867 A057462 ------- ------- ------- ------- ------- -------
  12 A079907 A251259 ------- ------- ------- A137654 ------- -------
  13 A297348 ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
  14 A273523 ------- ------- ------- ------- ------- ------- -------
  15 ------- ------- ------- ------- ------- ------- ------- -------
  16 ------- ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
Cf. (smallest k such that these forms are prime) A122396 (a1(b)+1 for prime b), A087139 (a2(b)+1 for prime b), A113516 (a5(b)), A076845 (a6(b)), A178250 (a7(b)).

a(n)=for(k=1,2^16,if(ispseudoprime((n-1)*n^k+1),return(k)))

cp's OEIS Frontend

A090669 Numbers k such that 7^k - 2 is a prime.

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A096305 Numbers k such that 7^k + 4 is prime.

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A217130 Numbers n such that 7^n + 6 is prime.

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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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A028499 6-hyperperfect numbers: n = 6*(sigma(n) - n - 1) + 1.

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