A197614 - OEIS

%I #18 Feb 21 2023 07:34:45

%S 44839,82193,630859553,2525696897,1910131806019,14899669504506112147,

%T 60135213227903643780817,4812219756324961,341826385983784841,

%U 3490785573251518581776138393,1025219842099467656125852928369,14472211420055197111499933838371

%N a(n) is the smallest prime of the form Sum_{j=1..k} prime(j)*prime(j+1)*...*prime(j+n).

%C Generalization of A197421.

%H Michel Marcus, <a href="/A197614/b197614.txt">Table of n, a(n) for n = 1..100</a>

%e For n=1, k=22 gives the smallest prime of the form Sum_{j=1..k} prime(j)*prime(j+1) = 44839 = 2*3 + 3*5 + 5*7 + ... + 79*83 where 79 = prime(22) and 83 = prime(23).

%p for n from 1 to 20 do:i:=0:p:=0:for j from 1 to 1000 while(i=0) do: uu:=1:for k from 0 to n do: uu:=uu*ithprime(j+k):od:p:=p+uu:if type(p,prime)=true then i:=1: printf(`%d, `,p):else fi:od:od:

%o (PARI) a(n) = my(k=1, p); while (!isprime(p=sum(j=1, k, prod(i=0, n, prime(j+i)))), k++); p; \\ _Michel Marcus_, Feb 21 2023

%Y Cf. A197421, A074745.

%K nonn

%O 1,1

%A _Michel Lagneau_, Oct 16 2011