A372648 a(n) is the least k for which A237196(k) = n.

4, 10, 43, 1, 2, 26, 3, 28, 13, 2311675, 8396, 12918370, 37697697, 4096146353, 31002004800, 278569264790

Offset

1,1

Comments

a(n) is the first k such that prime(k) + the product of the first n primes other than prime(k) is composite, while for j < n, prime(k) + the product of the first j primes other than prime(k) is prime.

Dickson's conjecture implies a(n) should exist.

Links

Table of n, a(n) for n=1..16.

Formula

A237196(a(n)) = n.

Example

a(3) = 43: A237196(43) = 3 because prime(43) = 191 and 2 + 191 = 193 and 2 * 3 + 191 = 197 are primes but 2 * 3 * 5 + 191 = 221 is not prime, and no smaller number than 43 works.

Maple

f:= proc(n) local j, p, t;
  t:= 1: p:= ithprime(n);
  for j from 1 do
    if j <> n then t:= t * ithprime(j) fi;
    if not isprime(t+p) then if j >= n then return j-1 else return j fi fi;
  od
end proc:
V:= Vector(8): count:= 0:
for  n from 1 while count < 8 do
  v:= f(n);
  if V[v] = 0 then V[v]:= n; count:= count+1 fi
od:
convert(V, list);

Crossrefs

Cf. A237196.

Sequence in context: A222475 A194993 A280907 * A332233 A149220 A149221

Adjacent sequences: A372645 A372646 A372647 * A372649 A372650 A372651

Keyword

nonn,more

Author

Robert Israel, May 08 2024

Extensions

a(10), a(12)-a(13) from Michael S. Branicky, May 08 2024

a(14) from Daniel Suteu, May 09 2024

a(15) from Michael S. Branicky, May 12 2024

a(16) from Michael S. Branicky, Jun 03 2024

Status

approved