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 1-3 of 3 results.

A066631 The sequence f(1), f(2), ... as defined in A068192.

Original entry on oeis.org

4, 8, 24, 120, 840, 9240, 120120, 2042040, 38798760, 1202761560, 34880085240, 802241960520, 32891920381320, 1414352576396760, 52331045326680120, 4657463034074530680, 274790319010397310120, 14563886907551057436360
Offset: 1

Views

Author

N. J. A. Sloane, Jun 10 2002

Keywords

Crossrefs

Cf. A068192.

Programs

  • PARI
    {a=4; for(n=1,18,print1(a,","); b=a-precprime(a-2); a=a*b)}

Extensions

Edited by Dean Hickerson and Klaus Brockhaus, Jun 10 2002

A068193 The prime indices of sequence A068192. (That sequence is conjectured to contain only primes.).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 11, 10, 9, 13, 14, 12, 24, 17, 16, 19, 22, 20, 33, 29, 52, 39, 46, 15, 23, 25, 18, 74, 26, 41, 44, 32, 36, 21, 56, 108, 34, 30, 37, 27, 53, 42, 78, 51, 113, 64, 43, 50, 58, 57, 31, 48, 67, 68, 47, 38, 83, 86, 65, 170, 103, 28, 77, 70, 69, 63, 129, 116
Offset: 1

Views

Author

Frank Buss (fb(AT)frank-buss.de), Feb 19 2002

Keywords

Comments

a(11)=9 because a(11) in sequence A068192 is 23 and this is the 9th prime number.

Crossrefs

Cf. A068192.

Extensions

Edited by Dean Hickerson, Jun 10 2002

A067836 Let a(1)=2, f(n)=a(1)*a(2)*...*a(n-1) for n>=1 and a(n)=nextprime(f(n)+1)-f(n) for n>=2, where nextprime(x) is the smallest prime > x.

Original entry on oeis.org

2, 3, 5, 7, 13, 11, 17, 19, 23, 37, 73, 29, 31, 43, 79, 53, 83, 67, 41, 47, 179, 149, 181, 103, 71, 59, 197, 167, 109, 137, 107, 251, 101, 157, 199, 283, 211, 277, 173, 127, 269, 61, 89, 271, 151, 191, 227, 311, 409, 577, 331, 281, 313, 307, 223, 491, 439, 233, 367
Offset: 1

Views

Author

Frank Buss (fb(AT)frank-buss.de), Feb 09 2002

Keywords

Comments

The terms are easily seen to be distinct. It is conjectured that every element is prime. Do all primes occur in the sequence?
All elements are prime and distinct through n=1000. - Robert Price, Mar 09 2013
All elements are prime and distinct through n=3724. - Dana Jacobsen, Feb 15 2015
With a(0) = 1, a(n) is the next smallest number not in the sequence such that a(n) + Product_{i=1..n-1} a(i) is prime. - Derek Orr, Jun 16 2015
A generalization of Fortunate's conjecture, cf. A005235. - M. F. Hasler, Nov 04 2024
Conjecture: there are infinitely many values of this sequence such that a(n) < n. - Davide Rotondo, Feb 28 2025

Links

Crossrefs

Cf. A062894 has the indices of the primes in this sequence. A071290 has the sequence of f's. Also see A067362, A068192.
Cf. A005235 (Fortunate numbers).

Programs

  • Mathematica
    <Jayanta Basu, Aug 10 2013 *)
  • MuPAD
    f := 1:for n from 1 to 50 do a := nextprime(f+2)-f:f := f*a:print(a) end_for
  • PARI
    v=[2];n=2;while(n<500,s=n+prod(i=1,#v,v[i]);if(isprime(s)&&!vecsearch(vecsort(v),n),v=concat(v,n);n=1);n++);v \\ Derek Orr, Jun 16 2015
  • Python
    from sympy import nextprime
def A067836_gen(): # generator of terms
    a, f = 2, 1
    yield 2
    while True:
        yield (a:=nextprime((f:=f*a)+1)-f)
A067836_list = list(islice(A067836_gen(),30)) # Chai Wah Wu, Sep 09 2023

Extensions

Edited by Dean Hickerson, Mar 02 2002
Edited by Dean Hickerson and David W. Wilson, Jun 10 2002
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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