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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 AUTHOR 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 March 18 08:02 EDT 2018. Contains 300719 sequences. (Running on oeis4.)