login
A073693
Product of next a(n) odd numbers plus 2 is prime.
3
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
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
Sequence in context: A077604 A112985 A293769 * A360916 A360918 A100261
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