A236019 Smallest number having at least n partitions that contain at least n primes.

0, 2, 5, 8, 10, 13, 15, 17, 20, 22, 24, 26, 28, 31, 33, 35, 37, 39, 41, 43, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Example

a(4) = 10: [2,2,2,2,1,1], [2,2,2,2,2], [3,2,2,2,1], [3,3,2,2].

Maple

b:= proc(n, i, t) option remember; `if`(n=0, `if`(t=0, 1, 0),
     `if`(i<1, 0, b(n, i-1, t) +`if`(i>n, 0,
      b(n-i, i, t -`if`(t>0 and isprime(i), 1, 0)))))
    end:
a:= proc(n) option remember; local k;
      for k from a(n-1) while b(k, k, n)<n do od; k
    end: a(0):=0:
seq(a(n), n=0..50);  # Alois P. Heinz, Jan 18 2014

Mathematica

$RecursionLimit = 1000; b[n_, i_, t_] := b[n, i, t] = If[n == 0, If[t == 0, 1, 0], If[i<1, 0, b[n, i-1, t] + If[i>n, 0, b[n-i, i, t - If[t>0 && PrimeQ[i], 1, 0]]]]]; a[n_] := a[n] = Module[{k}, For[k = a[n-1], b[k, k, n] < n, k++]; k]; a[0] = 0; Table[a[n], {n, 0, 61}] (* Jean-François Alcover, Jan 27 2014, after Alois P. Heinz *)

Crossrefs

Cf. A000041, A002095, A235945, A236444 (complement).

Sequence in context: A286808 A121294 A039770 * A247426 A047618 A236535

Adjacent sequences: A236016 A236017 A236018 * A236020 A236021 A236022

Keyword

nonn

Author

J. Stauduhar, Jan 18 2014

Extensions

More terms from Alois P. Heinz, Jan 18 2014

Status

approved