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.

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A007459 Higgs's primes: a(n+1) = smallest prime > a(n) such that a(n+1)-1 divides the product (a(1)...a(n))^2.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 43, 47, 53, 59, 61, 67, 71, 79, 101, 107, 127, 131, 139, 149, 151, 157, 173, 181, 191, 197, 199, 211, 223, 229, 263, 269, 277, 283, 311, 317, 331, 347, 349, 367, 373, 383, 397, 419, 421, 431, 461, 463, 491, 509, 523, 547, 557, 571
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Named after the British mathematician Denis A. Higgs (1932-2011). - Amiram Eldar, Jun 05 2021
No prime of the form a*b^k + 1 (those in A089200) with a > 0, b > 1 and k > 2 is a Higgs's prime. - Mauro Fiorentini, Aug 08 2023

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A057447, A057448, A057459, A089200, A282027.

Programs

  • Haskell
    a007459 n = a007459_list !! (n-1)
a007459_list = f 1 a000040_list where
  f q (p:ps) = if mod q (p - 1) == 0 then p : f (q * p ^ 2) ps else f q ps
-- Reinhard Zumkeller, Apr 14 2013
  • Maple
    a:=[2]; P:=1; j:=1;
for n from 2 to 32 do
P:=P*a[n-1]^2;
  for i from j+1 to 250 do
  if (P mod (ithprime(i)-1)) = 0 then
  a:=[op(a),ithprime(i)]; j:=i; break; fi;
od:
od:
a; # N. J. A. Sloane, Feb 12 2017
  • Mathematica
    f[ n_List ] := (a = n; b = Apply[ Times, a^2 ]; d = NextPrime[ a[ [ -1 ] ] ]; While[ ! IntegerQ[ b/(d - 1) ] || d > b, d = NextPrime[ d ] ]; AppendTo[ a, d ]; Return[ a ]); Nest[ f, {2}, 75 ]
nxt[{p_,a_}]:=Module[{np=NextPrime[a]},While[PowerMod[p,2,np-1] != 0,np = NextPrime[np]];{p*np,np}]; NestList[nxt,{2,2},60][[All,2]] (* Harvey P. Dale, Jul 09 2021 *)
  • PARI
    step(v)=my(N=vecprod(v)^2);forprime(p=v[#v]+1,,if(N%(p-1)==0,return(concat(v,p))))
first(n)=my(v=[2]);for(i=2,n,v=step(v));v \\ Charles R Greathouse IV, Jun 11 2015

Extensions

More terms from David W. Wilson
Definition clarified by N. J. A. Sloane, Feb 12 2017

A282027 a(n+1) = smallest prime p > a(n) such that p-1 divides a(1)*a(2)*...*a(n); or if no such prime p exists, then a(n+1) = smallest prime > a(n).

Original entry on oeis.org

2, 3, 7, 43, 47, 283, 659, 1319, 1699, 9227, 11887, 55399, 71359, 159707, 396719, 558643, 793439, 794039, 1117379, 1117943, 1143887, 2235887, 5554067, 6707747, 6863323, 13734803, 15667447, 16663963, 18214099, 20123239, 45196799, 46954223, 55937239, 93908447
Offset: 1

Views

Author

N. J. A. Sloane, Feb 13 2017

Keywords

Links

Crossrefs

Inspired by A007459 and A057459.

Programs

  • Maple
    A[1]:= 2: P:= 1:
for n from 2 to 30 do
  P:= A[n-1]*P;
  p0:= nextprime(A[n-1]);
  p:= p0;
  while p-1 <= P and P mod (p-1) <> 0 do
    p:= nextprime(p)
  od:
  if p-1 > P then A[n]:= p0
  else A[n]:= p
  fi;
od:
seq(A[i],i=1..30); # Robert Israel, Mar 17 2017
  • PARI
    lista(nn) = {my(d, k, m, t, v=List([2])); for(n=2, nn, k=1; m=oo; while((d=prod(i=1, t=k, v[i]))m || t==n-1, t++); forsubset([t, k], w, if(ispseudoprime(d=prod(i=1, k, v[w[i]])+1) && d>v[n-1], m=min(m, d)))); listput(v, if(mJinyuan Wang, Nov 21 2020

Extensions

Corrected and extended by Robert Israel, Mar 17 2017
More terms from Jinyuan Wang, Nov 21 2020
Showing 1-2 of 2 results.

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

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