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Initial primes of sets of 8 consecutive primes all different by modulo 30.
1

%I #12 Oct 09 2014 16:49:18

%S 2,3,5,7,11,13,17,19,47,499,673,677,769,1277,1279,1327,1697,2357,3163,

%T 3907,4057,4133,4909,5479,5669,6047,7283,9349,9533,9539,9547,9923,

%U 10667,11149,11159,12277,12841,17167,17431,17443,21101,21379,22549,22567,22993,24181,24337,24659,24671,25219,26161

%N Initial primes of sets of 8 consecutive primes all different by modulo 30.

%H Zak Seidov, <a href="/A248199/b248199.txt">Table of n, a(n) for n = 1..7000</a>

%H A. Granville and G. Martin, <a href="http://www.arXiv.org/abs/math.NT/0408319">Prime number races</a>, arXiv:math/0408319 [math.NT], 2004.

%e 47 is a term because 8 consecutive primes {47, 53, 59, 61, 67, 71, 73, 79} are congruent to {17, 23, 29, 1, 7, 11, 13, 19} mod 30; all distinct by modulo 30.

%o (PARI) isok(n) = {v = []; for (i=0, 7, pm = prime(i+n) % 30; if (! vecsearch(v, pm), v = vecsort(concat(v, pm)), return (0));); return (1);}

%o lista(nn) = {forprime(p=2, nn, if (isok(primepi(p)), print1(p, ", ")););} \\ _Michel Marcus_, Oct 06 2014

%Y Cf. A095959 (primes modulo 30).

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 03 2014