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A073125 a(n) is the least prime p(s) such that prime(s+n) - prime(s) is divisible by n. 3

%I #15 Jul 31 2017 03:25:45

%S 2,3,17,5,17,5,13,29,2,13,17,11,7,11,7,7,11,7,7,67,5,47,193,43,3,3,5,

%T 53,173,41,181,31,181,41,211,31,211,181,113,29,173,13,173,19,229,181,

%U 197,17,193,13,113,17,113,619,191,13,179,173,167,743,1499,7,1627,733

%N a(n) is the least prime p(s) such that prime(s+n) - prime(s) is divisible by n.

%H Michael De Vlieger, <a href="/A073125/b073125.txt">Table of n, a(n) for n = 1..1000</a>

%e n=1: a(1)=2 because 3 - 2 = 1 is divisible by 1.

%e n=10: a(10) = 13 = p(6) because p(6+10) - 13 = p(16) - 13 = 53 - 13 = 40 is divisible by 10.

%t Table[s = 1; While[! Divisible[Prime[s + n] - Set[p, Prime@s], n], s++]; p, {n, 64}] (* _Michael De Vlieger_, Jul 30 2017 *)

%o (PARI) a(n) = {s = 1; while ((prime(s+n) - prime(s)) % n, s++); prime(s);} \\ _Michel Marcus_, Dec 26 2013

%Y Cf. A073126, A073127.

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 16 2002

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