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A007459 Higgs' primes: a(n+1) = next prime such that a(n+1)-1 | (a(1)...a(n))^2.
(Formerly M0660)
7
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

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

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

MATHEMATICA

NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; 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

CROSSREFS

Cf. A057447, A057448 & A057459.

Sequence in context: A042987 A089189 A097375 * A129944 A176162 A152900

Adjacent sequences:  A007456 A007457 A007458 * A007460 A007461 A007462

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from David W. Wilson

STATUS

approved

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Last modified December 20 02:59 EST 2014. Contains 252240 sequences.