A175193 - OEIS

%I #20 Dec 02 2017 10:14:21

%S 1,2,2,3,2,3,2,4,3,2,3,3,2,4,3,3,2,3,3,2,3,4,3,4,3,2,3,2,5,4,4,3,2,4,

%T 2,3,3,5,3,3,2,9,2,3,2,4,5,3,2,5,3,2,7,3,3,3,2,3,3,2,4,4,3,2,4,8,3,5,

%U 2,4,3,4,3,3,5,3,5,4,5,4,2,5,2,3,4,3,5,3,2,4,4,4,5,7,4,3,6,2,4,3,4,3,3,2,3

%N a(n) is the smallest positive integer such that (the n-th prime)+a(n)! is prime, or -1 if no such prime exists.

%C A175194(n) = a(n)!.

%H Michael De Vlieger, <a href="/A175193/b175193.txt">Table of n, a(n) for n = 1..10000</a>

%H Michael De Vlieger, <a href="/A175193/a175193.txt">First positions of values and records in a(n).</a>

%F A092789(n) = A000040(n) + a(n)!.

%e From _Michael De Vlieger_, Nov 24 2017: (Start)

%e Records and their indices in a(n):

%e     i          n   a(n)

%e    --------------------

%e     1        1      1

%e     2        2      2

%e     3        4      3

%e     4        8      4

%e     5       29      5

%e     6       42      9

%e     7      233     10

%e     8      254     42

%e     9     4508     49

%e    10     7003    124

%e    11     7385    276

%e    12    60650    311

%e    13    97146    542

%e (End)

%t Fold[Append[#1, SelectFirst[Range[12], Function[k, PrimeQ[Prime[#2] + k!]]]] &, {1}, Range[2, 105]] (* _Michael De Vlieger_, Nov 24 2017 *)

%o (PARI) a(n) = {my(k = 1, p = prime(n)); while (!isprime(p + k!), k++); k;} \\ _Michel Marcus_, Nov 25 2017

%Y Cf. A082470, A092789, A175194.

%K nonn

%O 1,2

%A _Leroy Quet_, Mar 01 2010

%E Extended by _Ray Chandler_, Mar 04 2010