A272041 Smallest integer that can be expressed as the sum of n primes in at least n distinct ways.
2, 10, 15, 18, 19, 22, 25, 27, 29, 32, 34, 36, 39, 42, 44, 46, 49, 51, 53, 55, 58, 60, 63, 65, 67, 69, 72, 74, 76, 78, 80, 83, 85, 87, 90, 92, 94, 96, 98, 100, 102, 105, 107, 109, 111, 113, 115, 117, 120, 122, 124, 126, 128, 131, 133, 135, 137, 139, 141, 143
Offset: 1
Keywords
Examples
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
Links
- Lars Blomberg and Giovanni Resta, Table of n, a(n) for n = 1..5000 (first 99 terms from Lars Blomberg)
Programs
-
Mathematica
a[n_] := Block[{k = 1}, While[Length@ Quiet@ IntegerPartitions[k,{n}, Prime@ Range@ PrimePi@ k, n] < n, k++]; k]; Array[a, 50]
Extensions
a(36)-a(60) from Lars Blomberg, Jul 18 2017
Comments