OFFSET
2,3
COMMENTS
The first prime number taken into consideration in the sequence is prime(2)=3, as 2 does not have a preceding prime.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 2..1000
EXAMPLE
a(5) = 7: there are 7 partitions of prime(5) = 11 into distinct parts not larger than prime(4) = 7: [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2], [5,3,2,1].
MAPLE
b:= proc(n, i) option remember; (m-> `if`(m<n, 0, `if`(m=n, 1,
b(n, i-1)+b(n-i, min(n-i, i-1)))))(i*(i+1)/2)
end:
a:= n-> (p-> b(p(n), p(n-1)))(ithprime):
seq(a(n), n=2..50); # Alois P. Heinz, Aug 29 2018
MATHEMATICA
b[n_, i_] := b[n, i] = Function[m, If[m < n, 0, If[m == n, 1, b[n, i - 1] + b[n - i, Min[n - i, i - 1]]]]][i(i+1)/2];
a[n_] := b[Prime[n], Prime[n - 1]];
a /@ Range[2, 50] (* Jean-François Alcover, Nov 30 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Pierandrea Formusa, Aug 29 2018
EXTENSIONS
a(26)-a(39) from Alois P. Heinz, Aug 29 2018
STATUS
approved