A175193 a(n) is the smallest positive integer such that (the n-th prime)+a(n)! is prime, or -1 if no such prime exists.

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, 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, 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

Offset: 1

Author

Leroy Quet, Mar 01 2010

Keywords

• nonn

Comments

A175194(n) = a(n)!.

Examples

			From _Michael De Vlieger_, Nov 24 2017: (Start)
Records and their indices in a(n):
    i          n   a(n)
   --------------------
    1        1      1
    2        2      2
    3        4      3
    4        8      4
    5       29      5
    6       42      9
    7      233     10
    8      254     42
    9     4508     49
   10     7003    124
   11     7385    276
   12    60650    311
   13    97146    542
(End)
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, First positions of values and records in a(n).

Crossrefs

Cf. A082470, A092789, A175194.

Programs

Mathematica

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

PARI

a(n) = {my(k = 1, p = prime(n)); while (!isprime(p + k!), k++); k;} \\ Michel Marcus, Nov 25 2017

Formula

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

Extensions

Extended by Ray Chandler, Mar 04 2010