A007749 -id:A007749 - cp's OEIS frontend

A139073 Smallest prime number of the form (n+k!)/n.

2, 2, 3, 7, 1009, 2, 5702401, 631, 4481, 13, 566092801, 3, 23452949585516450807808000001, 259201, 337, 2521, 3553839003727872684550301886383176323956736000000001, 41

Offset: 1

Artur Jasinski, Apr 07 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 1..58

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A136019, A136020, A136026, A136027, A137390, A139056-A139066, A139068, A139070-A139075.

a = {}; Do[ k = 1; While[ ! PrimeQ[ (k! + n)/n ], k++ ]; AppendTo[ a, (k! + n)/n ], {n, 1, 100} ]; a [Corrected May 06 2008]

a(n)=my(k,t);until(denominator(t=k++!/n+1)==1&&ispseudoprime(t),);t \\ Charles R Greathouse IV, Jul 19 2011

a(n) = (n + A139072(n)!)/n. - Amiram Eldar, Oct 14 2024

A139091 a(n) = largest prime divisor of the number prime(n)!/9 + 1.

Original entry on oeis.org

17, 827, 22319071, 1718296754087, 35662591735219, 477262171871, 1609727002420791262479701, 146215297537890243023, 2020914387433686758547638152441, 1073774770807266077323

Offset: 4

Artur Jasinski, Apr 08 2008

nonn

Amiram Eldar, Table of n, a(n) for n = 4..26

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A136019, A136020, A136026, A136027, A139089-A139092.

a = {}; Do[w = FactorInteger[(Prime[n]! + 9)/9]; AppendTo[a, Last[w][[1]]], {n, 4, 16}]; a

A258866 Numbers k such that k!! - 1024 is prime.

Original entry on oeis.org

11, 17, 31, 39, 53, 93, 95, 381, 727, 867, 1229, 1573, 3161, 4293, 5635, 7077, 7093, 8861, 37401

Offset: 1

Robert Price, Nov 06 2015

Corresponding primes are 9371, 34458401, ... .

a(20) > 50000.

Joe McLean, Interesting Sources of Probable Primes

Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772.

Select[Range[0, 50000], If[#!! - 1024 > 0, PrimeQ[#!! - 1024]] &]

A259045 Numbers n such that n!! - 2^6 is prime.

Original entry on oeis.org

7, 9, 11, 17, 21, 27, 29, 39, 43, 45, 67, 145, 173, 613, 833, 1449, 1703, 1719, 2673, 19661, 36095, 37837, 37845

Offset: 1

Robert Price, Jun 17 2015

a(24) > 50000.

C. K. Caldwell, The Prime Glossary, multifactorial prime
Joe McLean, Interesting Sources of Probable Primes

Cf. A007749, A094144, A123910, A257864 (other forms of n!!-2^k)

Cf. A080778, A076185, A076186, A076188, A076189, A076190, A076193, A076194, A076195, A076196, A076197 (other forms of n!!+2^k)

Select[Range[0, 50000], #!! - 64 > 0 && PrimeQ[#!! - 64] &]
Select[Range[4, 6000], PrimeQ[#!! - 64] &] (* Vincenzo Librandi, Jun 18 2015 *)

A259359 Numbers n such that n!!-8 is prime.

Original entry on oeis.org

5, 7, 9, 19, 41, 43, 83, 89, 91, 143, 299, 307, 341, 381, 585, 995, 1019, 1027, 2043, 4301, 6275, 11157, 11621, 12315, 17505, 24771, 30535, 38635

Offset: 1

Robert Price, Jun 24 2015

Corresponding primes are 7, 97, 937, 654729067, 13113070457687988603440617, ... .

a(29) > 50000.

Joe McLean, Interesting Sources of Probable Primes

Cf. A006882, A007749, A094144, A123910, A258616.

Mathematica
```
Select[Range[5,1000],PrimeQ[#!!-8]&]
```

A265114 Numbers n such that n!! - 2^8 is prime.

Original entry on oeis.org

11, 15, 21, 27, 31, 53, 59, 71, 87, 91, 99, 129, 219, 337, 507, 695, 893, 1033, 1961, 2381, 3237, 3485, 6151, 8981, 17873, 18163, 33621, 38543

Offset: 1

Robert Price, Dec 01 2015

Corresponding primes are 10139, 2026769, 13749310319, 213458046676619, 191898783962510369, ...

a(29) > 50000. - Robert Price, May 08 2015

Joe McLean, Interesting Sources of Probable Primes

Cf. A007749, A094144.

Select[Range[8, 50000], PrimeQ[#!! - 256] &]

is(n)=ispseudoprime(n!! - 2^8) \\ Anders Hellström, Dec 02 2015

df(n) = if( n<0, 0, my(E); E = exp(x^2 / 2 + x * O(x^n)); n! * polcoeff( 1 + E * x * (1 + intformal(1 / E)), n));
for(n=1, 1e3, if(ispseudoprime(df(n) - 2^8), print1(n , ", "))) \\  Altug Alkan, Dec 03 2015

A267029 Numbers n such that n!!! - 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

Original entry on oeis.org

16, 17, 34, 38, 49, 62, 74, 97, 125, 137, 146, 178, 188, 235, 664, 863, 916, 1988, 2059, 2837, 5353, 5489, 7483, 9344, 12631, 13796, 17122, 23134, 30409, 33077

Offset: 1

Robert Price, Jan 09 2016

Corresponding primes are 38557, 189757, 17961239276317, 3091650738156317, ... .

a(31) > 50000.

			16!3 - 3^9 = 16*13*10*7*4*1 - 19683 = 58240 - 19683 = 38557 is prime, so 16 is in the sequence.

Henri & Renaud Lifchitz, PRP Records. Search for n!3-19683.
Joe McLean, Interesting Sources of Probable Primes

Cf. A006882, A007749, A094144, A123910, A258452, A258616, A262772, A261145, A265201.

MultiFactorial[n_, k_] := If[n < 1, 1, If[n < k + 1, n, n*MultiFactorial[n - k, k]]];
Select[Range[15, 50000], PrimeQ[MultiFactorial[#, 3] - 3^9] &]
Select[Range[12,33100],PrimeQ[Times@@Range[#,1,-3]-19683]&] (* Harvey P. Dale, Jan 25 2021 *)

A108420 Numbers k such that k!! - prime(k) is prime.

Original entry on oeis.org

14, 20, 54, 56, 144, 206, 212, 436, 1610, 4450, 4512, 5202, 6684, 14318

Offset: 1

Amineh Farzannia (afarzannia(AT)yahoo.com), Jul 06 2005

There is no further term up to 8800. - Farideh Firoozbakht, Aug 19 2005

			14 is a term since 14!! - prime(14) = 645120 - 43 = 645077 is prime.

Cf. A006882, A007749, A064401.

Select[Range[1610], PrimeQ[ #!! - Prime[ # ]] &]

More terms from Farideh Firoozbakht, Aug 19 2005

Name corrected, term 3 removed, and a(14) from Michael S. Branicky, Jan 03 2025

A122719 Primes p such that (2p)!! - 1 is prime.

Original entry on oeis.org

2, 3, 13, 41, 59, 97, 107, 421, 1663, 22159

Offset: 1

Alexander Adamchuk, Sep 23 2006

a(n) are the primes from A091415[n] = {2,3,4,8,13,32,41,45,59,97,107,364,421,...} Numbers n such that n!*2^n - 1 is prime. Corresponding primes of the form (2p)!! - 1 are {3,5,270269,26226140915375977206881249, 58431212742946338570036120182498518593749,...}

No other terms up to 3000. - Stefan Steinerberger, Sep 09 2007

Cf. A007749, A117141, A091415.

Select[Prime[Range[651]],PrimeQ[(2#)!!-1]&]

a(9) from Stefan Steinerberger, Sep 09 2007

a(10) from Robert Price, Nov 26 2013

A139090 a(n) = smallest prime divisor of the number prime(n)!/9 + 1.

Original entry on oeis.org

3, 31, 31, 23, 379, 83, 610301, 293, 101, 47, 281, 127, 278174297, 2971, 109, 5090615254324820333, 46411, 106087, 269, 288931, 59047158151, 120871, 373, 19140822523, 56595118147, 1708207, 331, 38749, 157, 2927, 2143

Offset: 4

Artur Jasinski, Apr 08 2008

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A136019, A136020, A136026, A136027, A139089-A139092.

a = {}; Do[w = FactorInteger[(Prime[n]! + 9)/9]; AppendTo[a, First[w][[1]]], {n, 4, 16}]; a
Table[FactorInteger[p!/9+1][[1,1]],{p,Prime[Range[4,35]]}] (* Harvey P. Dale, Sep 19 2020 *)

More terms from Jon E. Schoenfield, Jul 16 2010

cp's OEIS Frontend

A139073 Smallest prime number of the form (n+k!)/n.

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A139091 a(n) = largest prime divisor of the number prime(n)!/9 + 1.

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A258866 Numbers k such that k!! - 1024 is prime.

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A259045 Numbers n such that n!! - 2^6 is prime.

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A259359 Numbers n such that n!!-8 is prime.

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A265114 Numbers n such that n!! - 2^8 is prime.

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A267029 Numbers n such that n!!! - 3^9 is prime, where n!3 = n!!! is a triple factorial number (A007661).

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A108420 Numbers k such that k!! - prime(k) is prime.

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A122719 Primes p such that (2p)!! - 1 is prime.

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