A186102 Smallest prime p such that p == n (mod prime(n)).

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.

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 A343170

Adjacent sequences: A186099 A186100 A186101 * A186103 A186104 A186105

Keyword

nonn

Author

Zak Seidov, Feb 12 2011

Status

approved