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A374873
Smallest primes p_1 where products m of n consecutive primes p_1..p_n are such that only p_1 < m^(1/n).
2
2, 3, 113, 3229, 15683, 736279, 8332427, 37305713, 4948884397, 6193302809, 316781230427
OFFSET
2,1
EXAMPLE
a(2) = 2 since m = 2*3 = 6 and 3 > sqrt(6).
a(3) = 3 since m = 3*5*7 = 105 and 5 > 105^(1/3).
a(4) = 113 since m = 113 * 127 * 131 * 137 = 257557397 and 127 > 257557397^(1/4), etc.
MATHEMATICA
k = 1; Table[r = Range[0, n - 1]; While[(Set[{p, q, m}, {#[[1]], #[[2]], Times @@ #}]; q < Surd[m, n]) &[Prime[k + r]], k++]; p, {n, 2, 6}]
PROG
(PARI) a(n) = {my(ps = vector(n, k, prime(k))); forprime(p = prime(n+1), , if(ps[2]^n > vecprod(ps), return(ps[1])); ps = concat(vecextract(ps, "^1"), p)); } \\ Amiram Eldar, Sep 23 2024
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Michael De Vlieger, Sep 19 2024
EXTENSIONS
a(10)-a(12) from Amiram Eldar, Sep 23 2024
STATUS
approved