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 1-5 of 5 results.

A057034 Difference between n!! and the first prime before n!! - 1.

Original entry on oeis.org

3, 2, 5, 2, 5, 4, 7, 4, 7, 4, 23, 2, 19, 2, 97, 2, 19, 64, 17, 62, 19, 4, 17, 58, 23, 64, 157, 122, 47, 106, 47, 4, 29, 146, 31, 64, 29, 8, 71, 8, 43, 32, 31, 128, 67, 122, 41, 2, 37, 146, 137, 122, 191, 142, 59, 128, 71, 284, 109, 274, 101, 218, 97, 32, 83, 158, 53, 166
Offset: 4

Views

Author

Robert G. Wilson v, Sep 09 2000

Keywords

Comments

Analogous to the lesser Fortunate numbers but unlike them, all entries are not prime. Must odd entries are powers of two and all even entries are primes.

Crossrefs

Cf. A006882, A057019.

Programs

  • Mathematica
    PrevPrime[ n_Integer ] := (k=n-1; While[ !PrimeQ[ k ], k-- ]; Return[ k ]); f[ n_Integer ] := (p = n!! - 1; q = PrevPrime[ p ]; Return[ p - q + 1 ]); Table[ f[ n ], {n, 4, 75} ]

A058020 Difference between lcm(1,..,n) and the smallest prime > lcm(1,...,n) + 1, where n runs over A000961, lcm(n) runs through A051451.

Original entry on oeis.org

3, 5, 5, 7, 11, 13, 11, 13, 31, 23, 19, 37, 41, 29, 31, 43, 53, 41, 53, 79, 59, 97, 59, 61, 113, 97, 179, 73, 73, 97, 103, 101, 109, 101, 229, 109, 139, 113, 227, 131, 191, 163, 139, 199, 151, 139, 181, 223, 229, 367, 239, 499, 251, 509, 251, 227, 373, 281, 233
Offset: 1

Views

Author

Labos Elemer, Nov 14 2000

Keywords

Comments

Analogous to Fortunate numbers and like them so far proved to be primes. This holds for x<=421: if Q is the first follower prime, then Q(421)-lcm(1,...421) = 557. For first some cases when 1+LCM is also a prime, the 2nd primes give 3,5,5,7,11,11,.. deviations, i.e. give primes.

Crossrefs

Cf. A000961, A003418, A051451, A057019, A037153, A035346, A005235, A054272, A055211, A037155, A045493, A038710 etc

Programs

  • PARI
    N=1; for(n=2,1e3, if(isprimepower(n,&p), N*=p; print1(nextprime(N+2)-N", "))) \\ Charles R Greathouse IV, Nov 18 2015

Extensions

Name corrected by Charles R Greathouse IV, Nov 18 2015

A076198 a(n)=least s>0 such that n!!-s is prime.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 4, 7, 4, 7, 4, 23, 2, 1, 2, 97, 2, 19, 64, 17, 62, 19, 4, 1, 58, 23, 64, 157, 122, 47, 106, 47, 4, 29, 146, 31, 64, 29, 8, 71, 8, 43, 32, 31, 128, 67, 122, 41, 2, 37, 146, 137, 122, 191, 142, 59, 128, 71, 284, 109, 274, 1, 218, 97, 32, 83, 158, 53, 166
Offset: 3

Views

Author

Zak Seidov, Nov 02 2002

Keywords

Comments

Unlike the case n!!+s in A057019, there is no apparent rule for s here.

Crossrefs

Cf. A057019.

A076199 a(n) equals the least s>0 such that n!! + s^2 is prime.

Original entry on oeis.org

1, 1, 2, 3, 2, 5, 2, 5, 8, 7, 2, 19, 4, 17, 58, 11, 2, 17, 8, 31, 32, 17, 8, 13, 4, 23, 4, 23, 2, 53, 86, 37, 32, 23, 164, 79, 86, 23, 2, 229, 94, 89, 2, 89, 4, 83, 4, 149, 134, 31, 8, 83, 4, 53, 206, 227, 206, 283, 64, 43, 274, 37, 128, 263, 214, 163, 146, 167, 326, 157, 178
Offset: 1

Views

Author

Zak Seidov, Nov 02 2002

Keywords

Crossrefs

Cf. A057019.

Programs

  • Mathematica
    sp[n_]:=Module[{np=NextPrime[n]},While[!IntegerQ[Sqrt[np-n]],np = NextPrime[ np]];Sqrt[np-n]]; sp/@(Range[80]!!) (* Harvey P. Dale, Aug 04 2014 *)

A076200 a(n) equals the least s>0 such that n!! + s^3 is prime, or 0 if there is no such prime.

Original entry on oeis.org

1, 1, 2, 0, 2, 5, 2, 5, 2, 11, 4, 17, 8, 43, 2, 19, 2, 19, 4, 13, 32, 23, 4, 47, 2, 37, 74, 23, 86, 43, 122, 149, 128, 19, 146, 29, 226, 31, 64, 53, 2, 23, 134, 43, 268, 103, 134, 59, 64, 43, 4, 101, 16, 61, 346, 229, 278, 103, 16, 41, 64, 127, 2, 181, 302, 151, 146, 191, 262
Offset: 1

Views

Author

Zak Seidov, Nov 02 2002

Keywords

Examples

			a(4)=0 because 4!! = A006882(4) = 8 has algebraic factorization 8 + s^3 = (2 + s) * (4 - 2*s + s^2), thus can never be prime for any s. - _Sean A. Irvine_, Mar 24 2025

Crossrefs

Cf. A006882, A057019.

Extensions

Missing a(4)=0 inserted by Sean A. Irvine, Mar 24 2025
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