OFFSET
1,1
COMMENTS
Initial terms found by exhaustive search in Excel.
LINKS
Lars Blomberg and Giovanni Resta, Table of n, a(n) for n = 1..5000 (first 99 terms from Lars Blomberg)
EXAMPLE
The sequence is defined here as starting at n=1 to avoid the term a(0). Even though there cannot be exactly zero ways to add zero primes, there is always at least one way to add 0 primes to get any n (i.e., the sum of itself for any nonprime or (1+..+1) for any prime), and zero would be the lowest such number.
Sum of 1 prime in 1 way: 2.
Sum of 2 primes in 2 ways: 3+7 = 5+5 = 10.
Sum of 3 primes in 3 ways: 3+5+7 = 5+5+5 = 2+2+11 = 15.
Sum of 4 primes in 4 ways: 2+2+3+11 = 2+2+7+7 = 3+3+5+7 = 3+5+5+5 = 18.
Sum of 60 primes in 61 ways, e.g.: 57*2 + 3 + 7 + 19 = 37*2 + 23*3 = 143. - Lars Blomberg, Jul 18 2017
MATHEMATICA
a[n_] := Block[{k = 1}, While[Length@ Quiet@ IntegerPartitions[k, {n}, Prime@ Range@ PrimePi@ k, n] < n, k++]; k]; Array[a, 50]
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Ryan, Apr 21 2016
EXTENSIONS
a(36)-a(60) from Lars Blomberg, Jul 18 2017
STATUS
approved