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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) = n iff n is prime.

LINKS

Zak Seidov, Table of n, a(n) for n = 1..10000

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

CROSSREFS

Cf. A061067, A061068, A064402, A076297, A076298, A076299, A076300.

Cf. A000040, A260416.

Sequence in context: A118064 A292024 A290093 * A170848 A078017 A169816

Adjacent sequences:  A186099 A186100 A186101 * A186103 A186104 A186105

KEYWORD

nonn

AUTHOR

Zak Seidov, Feb 12 2011

STATUS

approved

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Last modified December 11 05:41 EST 2017. Contains 295868 sequences.