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.

A089538 A085747 indexed by A000040.

Original entry on oeis.org

2, 1, 2, 0, 0, 0, 0, 0, 3, 0, 2, 7, 0, 0, 4, 1, 2, 9, 0, 0, 5, 10, 2, 0, 0, 0, 12, 0, 13, 1, 8, 5, 5, 0, 4, 2, 13, 0, 6, 31, 15, 17, 1, 12, 3, 12, 17, 0, 1, 21, 17, 22, 21, 0, 0, 18, 0, 12, 0, 18, 11, 12, 14, 4, 23, 20, 8, 4, 27, 8, 0, 28, 12, 39, 0, 27, 2, 21, 29, 25
Offset: 1

Views

Author

Ray Chandler, Nov 09 2003

Keywords

Crossrefs

Cf. A085747, A089539, A089540, A089541.

Formula

a(n)=k such that A085747(n)=A000040(k) if A085747(n) is prime, otherwise 0.

Extensions

More terms from Max Alekseyev, Jun 17 2011

A089539 a(n) is the least semiprime > n!.

Original entry on oeis.org

4, 4, 9, 25, 121, 721, 5041, 40321, 362885, 3628801, 39916803, 479001617, 6227020801, 87178291201, 1307674368007, 20922789888002, 355687428096003, 6402373705728023, 121645100408832001, 2432902008176640001, 51090942171709440011, 1124000727777607680029, 25852016738884976640003
Offset: 1

Views

Author

Ray Chandler, Nov 09 2003

Keywords

Crossrefs

Cf. A001358, A085747, A089538, A089540, A089541, A089542.

Programs

  • Mathematica
    lsn[n_]:=Module[{sp=n!+1},While[PrimeOmega[sp]!=2,sp++];sp]; Array[lsn,25] (* Harvey P. Dale, Mar 30 2024 *)

Formula

a(n) = n! + A085747(n).

Extensions

Better name, more terms from Jinyuan Wang, Jul 31 2021

A089540 Lesser prime factor of semiprimes in A089539.

Original entry on oeis.org

2, 2, 3, 5, 11, 7, 71, 61, 5, 11, 3, 97, 83, 23, 7, 2, 3, 263, 71, 20639383, 11, 281421719, 3, 811, 401, 1697, 110298581317, 29, 33619, 2, 19, 11, 11, 67411, 7, 3, 126397507816417, 14029308060317546154181, 13, 9649, 53, 2044687972231331951
Offset: 1

Views

Author

Ray Chandler, Nov 09 2003

Keywords

Crossrefs

Cf. A085747, A089538, A089539, A089541.

A089541 Greater prime factor of semiprimes in A089539.

Original entry on oeis.org

2, 2, 3, 5, 11, 103, 71, 661, 72577, 329891, 13305601, 4938161, 75024347, 3790360487, 186810624001, 10461394944001, 118562476032001, 24343626257521, 1713311273363831, 117876683047, 4644631106519040001, 3994008464491
Offset: 1

Views

Author

Ray Chandler, Nov 09 2003

Keywords

Crossrefs

Cf. A085747, A089538, A089539, A089540.

A181764 Numbers n such that n!+1 is a product of two distinct prime numbers.

Original entry on oeis.org

6, 8, 10, 13, 14, 19, 20, 24, 25, 26, 28, 34, 38, 48, 54, 55, 59, 71, 75, 92, 109, 114, 115
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Nov 13 2010

Keywords

Comments

n! + 1 must be the product of two distinct prime numbers and also the product of only two prime numbers counted with multiplicity. Thus, 12 is NOT a term of the sequence because 12! + 1 = 13*13*2834329. - Harvey P. Dale, Jul 22 2019
Other terms in this sequence: 392, 551, 601, 770, 772, 878, 1033, 1320, 1831, 2620, 2808, 3752, 4233, 4616, 4984, 7260. - Chai Wah Wu, Feb 28 2020

Examples

			6!+1=7*103; 8!+1=61*661; 10!+1=11*329891; 13!+1=83*75024347; 14!+1=23*3790360487; 19!+1=71*1713311273363831;..

Links

Crossrefs

Cf. A033312, A038507, A078781, A085692, A085747, A088332.
Subsequence of A078778.

Programs

  • Mathematica
    fQ[n_]:=Last/@FactorInteger[n]=={1,1}; Select[Range[40], fQ[#!+1]&]

Extensions

Extended by D. S. McNeil, Nov 13 2010
One more term (114) (factored by Womack et al.) from Sean A. Irvine, May 25 2015
One more term (115) (factored by Womack et al.) from Sean A. Irvine, Feb 08 2016

A114187 Difference between first semiprime >= n! and n!. Least k such that n!+k is semiprime.

Original entry on oeis.org

3, 3, 2, 0, 1, 1, 1, 1, 1, 5, 1, 3, 17, 1, 1, 7, 2, 3, 23, 1, 1, 11, 29, 3, 1, 1, 1, 37, 1, 41, 2, 19, 11, 11, 1, 7, 3, 41, 1, 13, 127, 47, 59, 2, 37, 5, 37, 59, 1, 2, 73, 59, 79, 73, 1, 1, 61, 118, 37, 1, 61
Offset: 0

Views

Author

Jonathan Vos Post, Feb 04 2006

Keywords

Comments

a(n) = 1 when n!+1 is a factorial prime.
A098147 is difference between first odd semiprime > 10^n and 10^n.
In this sequence, does 1 occur infinitely often (next with n = 71, 75)? If not 0 (for n=3) or 1, a(n) = k must be a prime other than 5.
Does every odd prime but 5 occur? Some of these take longer to factor, when both prime factors are large, such as n = 37, 38, 42, 47, 50, 54.
Essentially the same as A085747. - Georg Fischer, Oct 07 2018

Examples

			a(0) = a(1) = 3 because 0! + 3 = 1! + 3 = 4 = 2^2 is semiprime (the only even example).
a(2) = 2 because 2! + 2 = 2 + 2 = 4 = 2^2 is semiprime.
a(3) = 0 because 3! + 0 = 6 = 2*3 is semiprime (6+3=9=3^2 so this term would be 3 if we required nonzero values).
a(4) = 1 because 4! + 1 = 24 + 1 = 25 = 5^2 is semiprime.
a(5) = 1 because 5! + 1 = 120 + 1 = 121 = 11^2 is semiprime.
a(6) = 1 because 6! + 1 = 720 + 1 = 721 = 7 * 103 is semiprime.
a(7) = 1 because 7! + 1 = 5040 + 1 = 5041 = 71^2 is semiprime.
a(8) = 1 because 8! + 1 = 40320 + 1 = 40321 = 61 * 661 is semiprime.
a(9) = 5 because 9! + 5 = 362880 + 1 = 362885 = 5 * 72577 is semiprime.
a(10) = 1 because 10! + 1 = 3628800 + 1 = 3628801 = 11 * 329891 is semiprime.

Crossrefs

Cf. A000142, A001358, A098147.

Formula

a(n) = minimum integer k such that n! + k is an element of A001358. a(n) = minimum integer k such that A000142(n) + k is an element of A001358.

Extensions

Data corrected by Giovanni Resta, Jun 14 2016
Showing 1-6 of 6 results.

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