A069870 Smallest prime that can be formed using a partition of n, or 0 if no such prime exists.

0, 2, 3, 13, 5, 0, 7, 17, 0, 19, 11, 0, 13, 59, 0, 79, 17, 0, 19, 137, 0, 139, 23, 0, 223, 179, 0, 127, 29, 0, 31, 131, 0, 277, 233, 0, 37, 137, 0, 139, 41, 0, 43, 359, 0, 379, 47, 0, 409, 149, 0, 151, 53, 0, 487, 353, 0, 157, 59, 0, 61, 359, 0, 163, 263, 0, 67, 167, 0, 367, 71, 0

Offset: 1

Author

Amarnath Murthy, Apr 21 2002

Keywords

• nonn
• base

Examples

			a(4) = 13 as the partitions of 4 are (4), (3, 1), ( 2, 2), (2, 1, 1) (1, 1, 1, 1). The primes that can be formed are 13, 31, 211 and 13 is the smallest prime using a partition.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A069869.

Programs

Mathematica

f[n_] := If[ PrimeQ@n, n, If[n > 5 && Mod[n, 3] == 0, 0, Block[{len = PartitionsP[n], p = IntegerPartitions[n], t = {}}, Do[ AppendTo[t, Select[FromDigits /@ Join @@@ IntegerDigits /@ Permutations@p[[i]], PrimeQ@# &]], {i, len}]; t = Union@Flatten@t; If[Length@t > 0, Min@t, 0]] ]]; Array[f, 72] (* Robert G. Wilson v, updated by Jean-François Alcover, Jan 29 2014 *)

Python

from collections import Counter
from sympy.utilities.iterables import partitions, multiset_permutations
from sympy import isprime
def A069870(n):
    d = 10**n
    smin, m = n+1, d
    if n==3 or n%3:
        for s in range(1,n+1):
            if s>smin:
                break
            m = min((k for k in (int(''.join(str(d) for d in a)) for p in partitions(n,m=s) for a in multiset_permutations(Counter(p).elements())) if isprime(k)),default=d)
            if mChai Wah Wu, Feb 21 2024

Extensions

Edited by David Wasserman, May 01 2003

Corrected by T. D. Noe, Nov 15 2006