A073693 Product of next a(n) odd numbers plus 2 is prime.

1, 1, 1, 4, 1, 1, 2, 2, 1, 1, 5, 1, 3, 10, 1, 1, 2, 1, 4, 1, 2, 2, 8, 3, 2, 2, 6, 3, 2, 1, 12, 2, 1, 3, 4, 1, 1, 7, 4, 1, 2, 1, 2, 6, 3, 6, 2, 1, 1, 7, 19, 26, 5, 2, 3, 1, 81, 3, 56, 28, 23, 2, 2, 17, 1, 6, 4, 9, 1, 2, 4, 1, 5, 9, 1, 7, 3, 1, 2, 16, 1, 6, 49, 7, 1, 2, 6, 3, 1, 6, 17, 3, 1

Offset

0,4

Comments

Group the odd numbers so that the product of the terms in each group + 2 is a prime: (1), (3), (5), (7, 9, 11, 13), (15), (17), (19, 21), (23, 25), (27), (29), ...; sequence gives the number of terms in each group.

a(n) is the least k >= 1 such that if sum_{i < n} a(i) = m, 2 + product_{m+1 <= i <=m+k} (2i-1) is prime. - Robert Israel, Sep 23 2024

Links

Robert Israel, Table of n, a(n) for n = 0..1263

Maple

m:= 0: A:= NULL: P:= 1: count:= 0:
for i from 1 do
  P:= P*(2*i-1);
  if isprime(P+2) then
    A:= A, i-m;
    m:= i; P:= 1;
    count:= count+1; if count = 101 then break fi;
  fi
od:
A; # Robert Israel, Sep 23 2024

Mathematica

t = {}; s = 1; c = 0; Do[s = s*i; c += 1; If[PrimeQ[s + 2], AppendTo[t, c]; s = 1; c = 0], {i, 1, 1200, 2}]; t (* Jayanta Basu, Jul 07 2013 *)

Prog

(PARI) o=1:for(k=1, 100, n=1:p=o:while(!isprime(p+2), o=o+2:p=p*o:n=n+1):o=o+2:print1(n", "))

Crossrefs

Cf. A073691, A073692.

Sequence in context: A077604 A112985 A293769 * A360916 A360918 A100261

Adjacent sequences: A073690 A073691 A073692 * A073694 A073695 A073696

Keyword

nonn

Author

Amarnath Murthy, Aug 12 2002

Extensions

Corrected and extended by Ralf Stephan, Mar 18 2003

Name clarified by Robert Israel, Sep 23 2024

Status

approved