A197614 a(n) is the smallest prime of the form Sum_{j=1..k} prime(j)*prime(j+1)*...*prime(j+n).

44839, 82193, 630859553, 2525696897, 1910131806019, 14899669504506112147, 60135213227903643780817, 4812219756324961, 341826385983784841, 3490785573251518581776138393, 1025219842099467656125852928369, 14472211420055197111499933838371

Offset

1,1

Comments

Generalization of A197421.

Links

Michel Marcus, Table of n, a(n) for n = 1..100

Example

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).

Maple

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:

Prog

(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

Crossrefs

Cf. A197421, A074745.

Sequence in context: A209909 A251790 A197421 * A202987 A183590 A230618

Adjacent sequences: A197611 A197612 A197613 * A197615 A197616 A197617

Keyword

nonn

Author

Michel Lagneau, Oct 16 2011

Status

approved