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A260416 The smallest prime that is greater than prime(n) and congruent to n mod prime(n).

%I A260416 #19 Aug 20 2015 19:31:29
%S A260416 3,5,13,11,71,19,41,103,101,97,73,197,587,229,109,281,607,79,421,233,
%T A260416 167,101,521,113,607,127,233,349,683,821,1301,163,307,173,631,1093,
%U A260416 1607,853,373,1597,757,223,1571,1009,439,643,2579,271,503,2111,983,769,1499,1811,569,2423,3823,3581,613,2027,1193,941,677,997
%N A260416 The smallest prime that is greater than prime(n) and congruent to n mod prime(n).
%H A260416 Reinhard Zumkeller, <a href="/A260416/b260416.txt">Table of n, a(n) for n = 1..10000</a>
%e A260416 Prime(4)=7, and the smallest prime that is greater than 7 and congruent to 4 mod 7 is 11, so a(4)=11.
%t A260416 lst={};Do[w=1;Label[begin];
%t A260416 If[PrimeQ[w*Prime[n]+n],AppendTo[lst,w*Prime[n]+n],w=w+1;Goto[begin]],{n,100}];lst
%o A260416 (PARI) first(m)={my(v=vector(m),t,p);for(i=1,m,t=i;while(1,p=prime(t);if((p-i)%prime(i)==0,v[i]=p;break,t++);));v;} /* _Anders Hellström_, Aug 11 2015 */
%o A260416 (Haskell)
%o A260416 a260416 n = a260416_list !! (n-1)
%o A260416 a260416_list = f 1 a000040_list where
%o A260416    f x (p:ps) = g ps where
%o A260416        g (q:qs) = if (q - x) `mod` p == 0 then q : f (x + 1) ps else g qs
%o A260416 -- _Reinhard Zumkeller_, Aug 20 2015
%Y A260416 Cf. A000040, A186102.
%K A260416 nonn
%O A260416 1,1
%A A260416 _Ivan N. Ianakiev_, Jul 25 2015