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 1-4 of 4 results.

A088250 a(n) is the smallest number k such that r*k + 1 is prime for all r = 1 to n.

Original entry on oeis.org

1, 1, 2, 330, 10830, 25410, 512820, 512820, 12960606120, 434491727670, 1893245380950, 71023095613470, 878232256181280, 11429352906540438870
Offset: 1

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Author

Amarnath Murthy, Sep 26 2003

Keywords

Comments

Conjectures: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.
Both conjectures follow from Dickson's conjecture. [Charles R Greathouse IV, Mar 14 2011]

Examples

			a(11) = 1893245380950 because all eleven numbers 1*1893245380950 + 1, 2*1893245380950 + 1, 3*1893245380950 + 1, ..., 10*1893245380950 + 1 & 11*1893245380950 + 1 are prime and 1893245380950 is the smallest number with such property.
		

Crossrefs

Programs

  • Mathematica
    a[n_] := Block[{k = If[n < 4, 1, 6], s}, s = k; While[! AllTrue[k Range[n] + 1, PrimeQ], k += s]; k]; Array[a, 8] (* Giovanni Resta, Mar 31 2017 *)

Extensions

Edited by Don Reble, Sep 29 2003
Entry revised by N. J. A. Sloane, Jan 05 2007
a(14) from Giovanni Resta, Mar 31 2017

A088252 n-th row of the following triangle contains smallest set of n primes which form n successive terms of an arithmetic progression from the 2nd to (n+1)th term with the first term 1. Sequence contains the leading diagonal.

Original entry on oeis.org

2, 3, 7, 1321, 54151, 152461, 3589741, 4102561, 116645455081, 4344917276701, 20825699190451, 852277147361641, 11417019330356641
Offset: 1

Views

Author

Amarnath Murthy, Sep 26 2003

Keywords

Comments

Conjectures: (1) Sequence is infinite. (2) For every n there are infinitely many arithmetic progressions with n successive primes.
A088252(n)=n*A088250(n)+1=n*A088251(n)-n+1. - Farideh Firoozbakht, Feb 21 2004

Examples

			2
2 3
3 5 7
331 661 991 1321
...
		

Crossrefs

Extensions

More terms from Farideh Firoozbakht, Feb 21 2004

A164325 a(n) is the smallest number m such that (2k-1)m+1 is prime for all 0

Original entry on oeis.org

1, 2, 2, 6, 1170, 64590, 25153800, 25153800, 4747505070, 207187349040, 6703860240000, 26997529639080, 1760354281625940, 1760354281625940, 10718654377787155800
Offset: 1

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Author

Farideh Firoozbakht, Sep 15 2009

Keywords

Crossrefs

Extensions

a(5) corrected by Zak Seidov, Sep 16 2009
a(10) and a(11) from Zak Seidov, Sep 17 2009
a(12)=26997529639080 from Zak Seidov, Sep 25 2009
a(13)-a(15) from Giovanni Resta, Apr 01 2017

A226935 Least prime p(1) beginning a chain of primes p(i) = i*p(i-1) - (i-1) for i = 2, 3, ..., n.

Original entry on oeis.org

2, 2, 2, 19, 19, 8629, 748669, 2506981, 228698251, 228698251
Offset: 1

Views

Author

Robin Garcia, Jun 22 2013

Keywords

Comments

Initial primes p(1) cannot be 3 mod 10 (except p(1) = 3) because p(2) would be 5 mod 10, not prime, and cannot be 7 mod 10 because p(4) would be 5 mod 10, not prime.

Examples

			a(5) --> p(1) = 19 because p(2) = 2*p(1) - 1 = 37, p(3) = 3*p(2) - 2 = 109, p(4) = 4*p(3) - 3 = 433, p(5) =5*p(4) - 4 = 2161 are primes.
		

Crossrefs

Programs

  • PARI
    \\ Find a(9)
    n=8; v=vector(n); forprime(p=2,10^9,i=0; a=2*p-1; b=3*a-2; c=4*b-3; d=5*c-4; e=6*d-5; f=7*e-6; g=8*f-7; h=9*g-8; if(isprime(a),i++; v[1]=a, v[1]=0); if(isprime(b), i++; v[2]=b, v[2]=0); if(isprime(c), i++; v[3]=c, v[3]=0); if(isprime(d), i++; v[4]=d, v[4]=0); if(isprime(e), i++; v[5]=e, v[5]=0); if(isprime(f), i++; v[6]=f, v[6]=0); if(isprime(g), i++; v[7]=g, v[7]=0); if(isprime(h), i++; v[8]=h, v[8]=0); if(i>n-1,print([p,v, i])))
    
  • PARI
    ct(p); my(i=2); while(isprime(p=i*p-i+1), i++); i
    a(n)=forprime(p=2,, if(ct(p)>n, return(p))) \\ Charles R Greathouse IV, Sep 27 2015

Formula

p(i) - p(i-1) = (i! - (i-1)!)*(p(1) - 1).
Showing 1-4 of 4 results.