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

3, 5, 13, 11, 71, 19, 41, 103, 101, 97, 73, 197, 587, 229, 109, 281, 607, 79, 421, 233, 167, 101, 521, 113, 607, 127, 233, 349, 683, 821, 1301, 163, 307, 173, 631, 1093, 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

Offset: 1

Author

Ivan N. Ianakiev, Jul 25 2015

Keywords

• nonn

Examples

			Prime(4)=7, and the smallest prime that is greater than 7 and congruent to 4 mod 7 is 11, so a(4)=11.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A186102.

Programs

Haskell

a260416 n = a260416_list !! (n-1)
a260416_list = f 1 a000040_list where
   f x (p:ps) = g ps where
       g (q:qs) = if (q - x) `mod` p == 0 then q : f (x + 1) ps else g qs
-- Reinhard Zumkeller, Aug 20 2015

Mathematica

lst={};Do[w=1;Label[begin];
If[PrimeQ[w*Prime[n]+n],AppendTo[lst,w*Prime[n]+n],w=w+1;Goto[begin]],{n,100}];lst

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 */