cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A139075 Primes p arising in A139074.

Original entry on oeis.org

3, 2, 3, 31, 1009, 2, 5702401, 631
Offset: 1

Views

Author

Artur Jasinski, Apr 08 2008, Apr 21 2008

Keywords

Comments

a(23) = (23+1579!)/23. - Andrew V. Sutherland, Apr 11 2008.
Smallest mother factorial prime p of order n, i.e. smallest prime of the form (p!+n)/n where p is prime.
For smallest daughter factorial prime p of order n see A139074.
For smallest father factorial prime p of order n see A139207.
For smallest son factorial prime p of order n see A139206.
a(9)=26737!/9+1 is a 106758 digit (probable) prime. Easily calculated but too large to enter here a(10)=13, a(11)=566092801, a(12)=11. [Robert Price, Jan 19 2011]

Crossrefs

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

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! + n)/n], k++ ]; AppendTo[a, Prime[(Prime[k]! + n)/n]], {n, 1, 8}]; a

A151901 Singular indices in A139074.

Original entry on oeis.org

9, 13, 22, 23, 72, 73, 74, 82, 83, 84, 85, 88
Offset: 1

Views

Author

Artur Jasinski, Apr 12 2008

Keywords

Comments

Definition: Singular indices in A139074 are numbers n such that it doesn't exist a prime p such that (n+p!)/n is prime or if this prime does exist then it is very big.

Crossrefs

Cf. A139074, A139206, A151900.

A137390 Numbers k for which (9 + k!)/9 is prime.

Original entry on oeis.org

8, 46, 87, 168, 259, 262, 292, 329, 446, 1056, 3562, 11819, 26737
Offset: 1

Views

Author

Artur Jasinski, Apr 09 2008

Keywords

Comments

No other k exists, for k <= 6000. - Dimitris Zygiridis (dmzyg70(AT)gmail.com), Jul 25 2008
The next number in the sequence, if one exists, is greater than 10944. - Robert Price, Mar 16 2010
Borrowing from A139074 another term in this sequence is 26737. There may be others between 10944 and 26737. - Robert Price, Dec 13 2011
There are no other terms for k < 26738. - Robert Price, Feb 10 2012

Examples

			a(11) = 3562 because 3562 is the 11th natural number for which k!/9 + 1 is prime. 3562 is the new term.

Crossrefs

Cf. A139068 (primes of the form (9 + k!)/9).
Cf. k!/m - 1 is a prime: A002982, A082671, A139056, A139199-A139205.
Cf. (m + k!)/m is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A139071.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 9)/9], AppendTo[a, n]], {n, 1, 500}]; a
  • PARI
    for(n=6,1e4,if(ispseudoprime(n!/9+1),print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011
  • PFGW
    ABC2 $a!/9+1
a: from 6 to 1000 // Jinyuan Wang, Feb 04 2020

Extensions

Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar
a(10) corrected from 1053 to 1056 by Dmitry Kamenetsky, Jul 12 2008
a(11) from Dimitris Zygiridis (dmzyg70(AT)gmail.com), Jul 25 2008
a(12)-a(13) from Robert Price, Feb 10 2012

A139206 Smallest son factorial prime p of order n: smallest p such that p!/n-1 is prime.

Original entry on oeis.org

3, 3, 29, 5, 5, 5, 7, 11, 17, 5, 19, 7, 13, 7, 5, 37, 139, 19
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008, Apr 24 2008

Keywords

Comments

For smallest daughter factorial prime p of order n (smallest p such that (p!+n)/n = p!/n + 1 is prime), see A139074.
a(19) is currently unknown, a(20)=5, a(21)=7, a(22)=19.
a(19)>10000, a(23)=71, a(24)=3361. [From Andrew V. Sutherland, Apr 23 2008]
a(25)=17, a(26)=223, a(27)=157, a(28)=7, a(29)=41, a(30)=5, a(31)=31, a(32)=71, a(33)=13, a(34)=37, a(35)=19, a(36)=7, a(37)=47, a(38)=53, a(39)=13, a(40)=5, a(41)=127, a(42)=13, a(43)=67, a(44)=11, a(45)=17, a(46)=43, a(47)=71, a(48)=11, a(49)=19, a(50)=29, a(51)=17, a(52)=17, a(53)>10000.
a(19)>25000, a(53)>25000. [From Sean A. Irvine, Nov 14 2010]
a(54)=11, a(55)=23, a(56)=7, a(57)=433.
a(58)=283, a(59)>1500, a(60..66)=(7,139,239,7,11,13,13), a(67), a(68) > 1300, a(69..72)=(29,7,83,13), a(73)>1000. [From M. F. Hasler, Nov 03 2013]
Sequence A151900 (tentatively?) lists "singular indices", i.e., those for which a(n) is difficult to find. - M. F. Hasler, Nov 03 2013

Crossrefs

Cf. A139074, A139189-A139198, A136019, A136020, A136026, A136027.

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! - n)/n], k++ ]; Print[a]; AppendTo[a, Prime[k]], {n, 1, 100}]; a (*Artur Jasinski*)
  • PARI
    a(n)=forprime(p=1,,p!%n==0 && ispseudoprime(p!/n-1) && return(p)) \\ - M. F. Hasler, Nov 03 2013

Extensions

Edited by M. F. Hasler, Nov 03 2013

A139207 Smallest father factorial prime p of order n = smallest prime of the form (p!-n)/n where p is prime.

Original entry on oeis.org

5, 2, 2947253997913233984847871999999, 29, 23, 19, 719, 4989599, 39520825343999, 11, 11058645491711999, 419, 479001599, 359, 7, 860234568201646565394748723848806399999999
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

For smallest daughter factorial prime p of order n (smallest p such that (p!+n)/n = p!/n + 1 is prime) see A139074.
For smallest son factorial prime p of order n = smallest prime of the form (p!-n)/n where p is prime see A139206.
For more terms see A139206.

Crossrefs

Cf. A139074, A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198, A136019, A136020, A136026, A136027.

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! - n)/n], k++ ]; Print[a]; AppendTo[a, (Prime[k]! - n)/n], {n, 1, 100}]; a

A151900 Singular indices in A139206.

Original entry on oeis.org

19, 24, 53, 59, 67, 68, 73
Offset: 1

Views

Author

Artur Jasinski, Apr 12 2008

Keywords

Comments

Definition: Singular indices in A139206 are numbers n for which there exists no prime p such that p!/n-1 is prime or, if such a prime p exists, it is very big.
I frown upon this "definition" and the notion of "very big", especially because A139206(24)=3361 seems to be considered to be "very big"(?!)... A more rigorous definition should be given. - M. F. Hasler, Nov 03 2013

Examples

			From _M. F. Hasler_, Nov 03 2013: (Start)
The first unknown term in A139206 is A139206(19), which is (if it exists) larger than 25000. Therefore a(1)=19.
The term A139206(24)=3361 is "quite large", therefore a(2)=24.
The next unknown term in A139206 is A139206(53), which is also larger than 25000, if it exists. Therefore a(3)=53. (End)

Crossrefs

Cf. A139074, A139206, A151901.

Extensions

Edited, corrected and extended by M. F. Hasler, Nov 03 2013
Showing 1-6 of 6 results.

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