OFFSET
1,1
COMMENTS
Sums of all distinct products of 3 out of 5 consecutive primes, starting with the n-th prime; value of 3rd elementary symmetric function on the 5 consecutive primes.
FORMULA
Let p = Prime(n), q = Prime(n+1), r = Prime(n+2), s = Prime(n+3) and t = Prime(n+4). Then a(n) = p q (r+s+t) + (p + q) r (s + t) + (p + q + r) s t.
MATHEMATICA
a = {}; Do[AppendTo[a, (Prime[x] Prime[x + 1] Prime[x + 2] + Prime[x] Prime[x + 1] Prime[x + 3] + Prime[x] Prime[x + 1] Prime[x + 4] + Prime[x] Prime[x + 2] Prime[x + 3] + Prime[x] Prime[x + 2] Prime[x + 4] + Prime[x] Prime[x + 3] Prime[x + 4] + Prime[x + 1] Prime[x + 2] Prime[x + 3] + Prime[x + 1] Prime[x + 2] Prime[x + 4] + Prime[x + 1] Prime[x + 3] Prime[x + 4] + Prime[x + 2] Prime[x + 3] Prime[x + 4])], {x, 1, 100}]; a
fcp[{p_, q_, r_, s_, t_}]:=p*q(r+s+t)+(p+q)r(s+t)+(p+q+r)s*t; fcp/@Partition[ Prime[ Range[40]], 5, 1] (* Harvey P. Dale, Sep 05 2014 *)
CROSSREFS
Cf. A001043, A034961, A034963, A034964, A127333, A127334, A127335, A127336, A127337, A127338, A127339, A127340, A127341, A127342, A127343, A127345, A127346, A127347, A127348, A127349, A127351, A037171, A034962, A034965, A082246, A082251, A070934, A006094, A046301, A046302, A046303, A046324, A046325, A046326, A046327, A127489.
KEYWORD
nonn
AUTHOR
Artur Jasinski, Jan 16 2007
EXTENSIONS
Edited and corrected by Franklin T. Adams-Watters, Jan 23 2007
STATUS
approved