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.

Previous Showing 21-25 of 25 results.

A257864 Numbers n such that n!! - 2^7 is prime.

Original entry on oeis.org

11, 13, 21, 47, 59, 77, 109, 129, 155, 163, 245, 337, 511, 1417, 3013, 3757, 4989, 8977, 12479, 12869
Offset: 1

Views

Author

Robert Price, May 11 2015

Keywords

Comments

a(21) > 50000. - Robert Price, May 11 2015
a(n) is odd. - Chai Wah Wu, May 12 2015

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 50000], #!! - 128 > 0 && PrimeQ[#!! - 128] &]
  • PARI
    is(n)=ispseudoprime(prod(i=0,(n-1)\2, n-2*i)-128) \\ Charles R Greathouse IV, May 11 2015
    
  • Perl
    use ntheory ":all"; use Math::GMPz;
    sub mf2 { my($n,$P)=(shift,Math::GMPz->new(1)); $P *= $n-($_<<1) for 0..($n-1)>>1; $P; }
    for (1..100000) { say if is_prob_prime(mf2($)-128) } # _Dana Jacobsen, May 13 2015
  • Python
    from gmpy2 import is_prime, mpz
    A257864_list, g, h = [], mpz(105), mpz(128)
    for i in range(9,10**5,2):
        g *= i
        if is_prime(g-h):
            A257864_list.append(i) # Chai Wah Wu, May 12 2015
    

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

Views

Author

Robert Price, Jun 17 2015

Keywords

Comments

a(24) > 50000.

Crossrefs

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

Programs

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

A374901 Numbers k such that k!^2 + ((k - 1)!^2) + 1 is prime.

Original entry on oeis.org

1, 3, 4, 6, 10, 11, 118, 271, 288, 441, 457, 2931, 5527, 6984, 9998, 10395, 13703
Offset: 1

Views

Author

Arsen Vardanyan, Jul 31 2024

Keywords

Comments

a(18) > 15000 - Karl-Heinz Hofmann, Aug 23 2024

Examples

			4 is a term, because 4!^2 + 3!^2 + 1 = 576 + 36 + 1 = 613 is a prime number.
		

Crossrefs

Programs

  • PARI
    is(k) = isprime((k!^2)+((k-1)!)^2+1);
    
  • Python
    from itertools import count, islice
    from sympy import isprime
    def A374901_gen(): # generator of terms
        f = 1
        for k in count(1):
            if isprime((k**2+1)*f+1):
                yield k
            f *= k**2
    A374901_list = list(islice(A374901_gen(),10)) # Chai Wah Wu, Oct 02 2024

Extensions

a(12)-a(14) from Michael S. Branicky, Aug 01 2024
a(15)-a(17) from Karl-Heinz Hofmann, Aug 23 2024

A110094 Startorial primes.

Original entry on oeis.org

2, 3, 5, 7, 23, 719, 5039, 1451521, 2903041, 5806081, 46448639, 92897281, 371589121, 10032906239, 30098718719, 270888468479, 812665405439, 7313988648961, 21941965946881, 89874292518420479
Offset: 1

Views

Author

Jonathan Vos Post, Sep 04 2005

Keywords

Comments

These are primes of the form A109834 startorials (base 10) +1 or -1. This is by analogy to factorial primes (A002981), superfactorial primes (A073828), hyperfactorial primes, ultrafactorial primes (comment in A046882), subfactorial primes (A100015), double factorial primes (A080778), multifactorial primes (A037083).

Crossrefs

Formula

{a(n)} = {A109834(k)+1 an element of A000040, or A109834(k)-1 an element of A000040, for some k}.

A274385 Double factorial primes: primes which are within 1 of a double factorial number.

Original entry on oeis.org

2, 3, 7, 47, 383, 10321919, 51011754393599, 1130138339199322632554990773529330319359999999, 73562883979319395645666688474019139929848516028923903999999999, 4208832729023498248022825567687608993477547383960134557368319999999999
Offset: 1

Views

Author

Arkadiusz Wesolowski, Jun 19 2016

Keywords

Examples

			a(2) = 3 = 2 + 1 = 2!! + 1 is the 2nd prime of that form.
a(4) = 47 = 2*4*6 - 1 = 6!! - 1 is the 4th prime of that form.
		

Crossrefs

Programs

  • Magma
    r:=91; I:=[1, 1]; lst1:=[n le 2 select I[n] else (n-1)*Self(n-2): n in [1..r]]; lst2:=[]; for c in [1..r] do a:=lst1[c]; for s in [-1..1 by 2] do p:=a+s; if IsPrime(p) and not p in lst2 then Append(~lst2, p); end if; end for; end for; lst2;
Previous Showing 21-25 of 25 results.