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

1,1

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

Cf. A054845, A054859.

Sequence in context: A065989 A299378 A031222 * A212160 A134861 A063610

Adjacent sequences: A272038 A272039 A272040 * A272042 A272043 A272044

Keyword

nonn

Author

Matthew Ryan, Apr 21 2016

Extensions

a(36)-a(60) from Lars Blomberg, Jul 18 2017

Status

approved