OFFSET
1,1
COMMENTS
If we consider the m-fold iterated "take sums of successive terms" operation acting on the primes, then for all m >= 1, the first term is always odd (and the only odd term); it is prime for m=1, 2, 4, 8, 21, 24, 27, 31, 40, 98,..., but not for m=3 (the present sequence). [Edited by M. F. Hasler, Jun 02 2017]
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
Let f(n) = prime(n) + prime(n+1) f1(n) = f(n)+f(n+1) : SS of order 1 Then f2(n) = f1(n)+f1(n) : SS of order 2 is the general term of this sequence.
a(n) = prime(n)+3*prime(n+1)+3*prime(n+2)+prime(n+3). - Robert Israel, Dec 28 2022
EXAMPLE
The first two terms of SS order 1 is 13 and 20. 13+20 = 33 the first term of the sequence.
MAPLE
Ss:= L -> L[1..-2]+L[2..-1]:
(Ss@@3)([seq(ithprime(i), i=1..100)]); # Robert Israel, Dec 28 2022
MATHEMATICA
Nest[ListConvolve[{1, 1}, #]&, Prime[Range[100]], 3] (* Paolo Xausa, Oct 31 2023 *)
PROG
(PARI) g(n) = for(x=1, n, print1(f2(x)", ")) f(n) = return(prime(n)+prime(n+1)) f1(n) = return(f(n)+f(n+1)) f2(n) = return(f1(n)+f1(n+1))
(PARI) A096278(n, m=3)=for(k=0, m, prime(n+k)*binomial(m, k)) \\ or, to get a list:
A096278_vec(Nmax, m=3, v=primes(Nmax+m))=sum(k=0, m, binomial(m, k)*v[1+k, k-1-m]) \\ Alternatively, do m times v=v[^1]+v[^-1]. - M. F. Hasler, Jun 02 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, Jun 22 2004
STATUS
approved