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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.
(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

REFERENCES

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

S. Burris and S. Lee, Tarski's high school identities, Amer. Math. Monthly 100 (1993), 231-236.

R. 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).

R. G. Wilson, V, Letter to N. J. A. Sloane, Oct. 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 ]

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

Cf. A057447, A057448, A057459, A282027.

Sequence in context: A042987 A089189 A097375 * A129944 A176162 A152900

Adjacent sequences:  A007456 A007457 A007458 * A007460 A007461 A007462

KEYWORD

nonn,nice,changed

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson

Definition clarified by N. J. A. Sloane, Feb 12 2017

STATUS

approved

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Last modified November 22 15:27 EST 2017. Contains 295089 sequences.