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

1,2

Comments

A175194(n) = a(n)!.

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).

Formula

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

Example

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)

Mathematica

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

Prog

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

Crossrefs

Cf. A082470, A092789, A175194.

Sequence in context: A338720 A320013 A299990 * A353861 A073093 A326196

Adjacent sequences: A175190 A175191 A175192 * A175194 A175195 A175196

Keyword

nonn

Author

Leroy Quet, Mar 01 2010

Extensions

Extended by Ray Chandler, Mar 04 2010

Status

approved