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A186102
Smallest prime p such that p == n (mod prime(n)).
4
3, 2, 3, 11, 5, 19, 7, 103, 101, 97, 11, 197, 13, 229, 109, 281, 17, 79, 19, 233, 167, 101, 23, 113, 607, 127, 233, 349, 29, 821, 31, 163, 307, 173, 631, 1093, 37, 853, 373, 1597, 41, 223, 43, 1009, 439, 643, 47, 271, 503, 2111, 983, 769, 53, 1811, 569, 2423
OFFSET
1,1
COMMENTS
a(n) = n iff n is prime.
EXAMPLE
Eighth prime is 19, and 103 is the smallest prime p such that p mod 19 is 8. Therefore a(8) = 103.
MATHEMATICA
k=200; Table[p=Prime[n]; m=n; While[!PrimeQ[m], m=m+p]; m, {n, k}]; (* For the first k terms. Zak Seidov, Dec 13 2013 *)
Flatten[With[{prs=Prime[Range[500]]}, Table[Select[prs, Mod[#, Prime[n]] == n&, 1], {n, 60}]]] (* Harvey P. Dale, Mar 30 2012 *)
PROG
(Magma) Aux:=function(n); q:=NthPrime(n); p:=2; while p mod q ne n do p:=NextPrime(p); end while; return p; end function; [ Aux(n): n in [1..70] ]; // Klaus Brockhaus, Feb 12 2011
(Sage) def A186102(n): np = nth_prime(n); return next(p for p in Primes() if p % np == n) # [D. S. McNeil, Feb 13 2011]
(Haskell)
a186102 n = f a000040_list where
f (q:qs) = if (q - n) `mod` (a000040 n) == 0 then q else f qs
-- Reinhard Zumkeller, Aug 21 2015
KEYWORD
nonn
AUTHOR
Zak Seidov, Feb 12 2011
STATUS
approved