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 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A073093 A326196 A222084 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

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Last modified August 3 08:20 EDT 2021. Contains 346435 sequences. (Running on oeis4.)