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

1,2

Links

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

Example

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.

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 *)

Prog

(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 m<d:
                smin=s
    if m == d:
        return 0
    else:
        return m # Chai Wah Wu, Feb 21 2024

Crossrefs

Cf. A069869.

Sequence in context: A336848 A336838 A051298 * A067180 A067182 A342667

Adjacent sequences: A069867 A069868 A069869 * A069871 A069872 A069873

Keyword

nonn,base

Author

Amarnath Murthy, Apr 21 2002

Extensions

Edited by David Wasserman, May 01 2003

Corrected by T. D. Noe, Nov 15 2006

Status

approved