cp's OEIS Frontend

A072063 Smallest prime of form prime(n)+k*n, k>0.

%I A072063 #16 Nov 27 2023 13:05:41
%S A072063 3,5,11,11,31,19,31,43,41,59,53,61,67,71,107,101,127,79,181,131,157,
%T A072063 101,313,113,197,127,157,163,167,173,251,163,269,173,359,223,379,239,
%U A072063 401,293,1163,223,277,281,467,337,587,271,521,379,641,499
%N A072063 Smallest prime of form prime(n)+k*n, k>0.
%C A072063 According to Dirichlet's theorem primes of form prime(n)+k*n exist for all n, as gcd(n, prime(n))=1.
%C A072063 Nontrivial least prime == prime(n) (mod n).
%H A072063 Robert Israel, <a href="/A072063/b072063.txt">Table of n, a(n) for n = 1..10000</a>
%e A072063 n=3, prime(3)=5: 5+1*3=8 is not prime, but 5+2*3=11, therefore a(3)=11 and A072064(3)=2.
%p A072063 f:= proc(n) local p,k,k0;
%p A072063   p:= ithprime(n);
%p A072063   if n::odd then k0:= 2 else k0:= 1 fi;
%p A072063   for k from k0 by k0 do
%p A072063     if isprime(p+k*n) then return p+k*n fi
%p A072063   od:
%p A072063 end proc:
%p A072063 f(1):= 3:
%p A072063 map(f, [$1..100]); # _Robert Israel_, Nov 27 2023
%t A072063 sp[n_]:=Module[{p=Prime[n],k=1},While[!PrimeQ[p+k*n],k++];p+k*n]; Array[ sp,60] (* _Harvey P. Dale_, Apr 19 2019 *)
%o A072063 (PARI) a072063(n) = {my (p=prime(n), j); for (k=1, oo, if(isprime(j=p+k*n), return(j)))}; \\ _Hugo Pfoertner_, Nov 27 2023
%Y A072063 Cf. A034694, A000040, A061068, A072064.
%Y A072063 Cf. A090471, A090472, A090473.
%K A072063 nonn
%O A072063 1,1
%A A072063 _Reinhard Zumkeller_, Jun 12 2002