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A007459
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Higgs' primes: a(n+1) = next prime such that a(n+1)-1 | (a(1)...a(n))^2.
(Formerly M0660)
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7
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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;
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OFFSET
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1,1
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REFERENCES
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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).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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MATHEMATICA
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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 ]
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PROG
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(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
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CROSSREFS
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Cf. A057447, A057448 & A057459.
Sequence in context: A042987 A089189 A097375 * A129944 A176162 A152900
Adjacent sequences: A007456 A007457 A007458 * A007460 A007461 A007462
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from David W. Wilson
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STATUS
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approved
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