

A069870


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


2



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
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OFFSET

1,2


LINKS



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 JeanFrançois Alcover, Jan 29 2014 *)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



EXTENSIONS



STATUS

approved



