login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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.
(Formerly M0660)
8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
Stanley Burris and Simon Lee, Tarski's high school identities, Amer. Math. Monthly, Vol. 100, No. 3 (1993), pp. 231-236.
Robert G. Wilson v, Note to N. J. A. Sloane with attachment, (Annotated scanned copy of The Am. Math. Mo. Vol. 100 No. 3 pp. 233, Mar. 1993).
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 *)
PROG
(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
(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
CROSSREFS
Sequence in context: A042987 A089189 A097375 * A129944 A176162 A152900
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
More terms from David W. Wilson
Definition clarified by N. J. A. Sloane, Feb 12 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 07:17 EDT 2024. Contains 370954 sequences. (Running on oeis4.)