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.

A071580 Smallest prime of the form k*a(n-1)*a(n-2)*...*a(1)+1.

Original entry on oeis.org

2, 3, 7, 43, 3613, 65250781, 5109197227031017, 21753246920584523633819544186061, 993727878334632126576336773629979379563850938567846991629270287
Offset: 1

Views

Author

Rick L. Shepherd, May 31 2002

Keywords

Comments

The former definition was "Smallest prime == 1 mod (a(n-1)*a(n-2)*...*a(1)) for n>=2 with a(1)=2."
a(6) through a(13), with digit lengths 8, 16, 32, 63, 127, 253, 507 and 1012, respectively, have been certified prime with Primo.
There is no need to use Elliptic curve primality proving (ECPP) to certify the primes. The primality of each term can be proved recursively with the "N-1 method" since the full factorization of a(n)-1 is known. - Jeppe Stig Nielsen, May 14 2023

Links

Crossrefs

Cf. A061092, A258081.

Programs

  • Maple
    P:= 1:
for n from 1 to 13 do
  for k from 1 do
     if isprime(k*P+1) then
       A[n]:= k*P+1;
       P:= P * A[n];
       break
     fi
  od
od:
seq(A[i],i=1..13); # Robert Israel, May 19 2015
  • Mathematica
    sp[{p_,a_}]:=Module[{k=1},While[!PrimeQ[k*p+1],k++];{p(p*k+1),p*k+1}]; NestList[sp,{2,2},10][[All,2]] (* Harvey P. Dale, Mar 04 2019 *)
  • PARI
    terms=13; v=vector(terms); p=2; v[1]=p; for(n=2,terms, q=p+1; while(!isprime(q), q=q+p); v[n]=q; p=p*q); v

Extensions

Definition reworded by Andrew R. Booker, May 19 2015

A090475 Beginning with 2, a(n+1) is the least prime == -1 (mod Product_{i=1..n} a(i) ).

Original entry on oeis.org

2, 3, 5, 29, 2609, 2269829, 20608503836279, 3397683442959574948323216959, 42930190020276065993287927763424183433168916230440704129, 1192530198055712826264639739575734950954723597893286538562918677849035900498296709057759892487138176511608345909
Offset: 1

Views

Author

Amarnath Murthy, Dec 02 2003

Keywords

Crossrefs

Cf. A090474, A090476, A071580, A258081.

Programs

  • PARI
    terms=12; p=2; print1("2, "); for(n=2, terms, q=p-1; while(!ispseudoprime(q), q=q+p); print1(q, ", "); p=p*q) \\ Serge Batalov, May 22 2015

Extensions

Corrected and extended by David Wasserman, Nov 16 2005

A263540 Values of k in A263539.

Original entry on oeis.org

1, 1, 1, 1, 1, 17, 25, 37, 265, 5, 93, 2395, 1443, 3935, 2757, 5865
Offset: 1

Views

Author

Jeppe Stig Nielsen, Oct 20 2015

Keywords

Crossrefs

Cf. A263539, A258081.

Programs

  • PARI
    terms=12; p=1; for(n=1, terms, q=p+2; while(!ispseudoprime(q), q+=2*p); print1((q-2)/p, ", "); p*=q)
Showing 1-3 of 3 results.

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

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