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A069869 Largest prime that is a concatenation of the parts of a partition of n, or 0 if no such prime exists. 5
0, 11, 3, 211, 2111, 0, 112111, 1111211, 0, 11131111, 1121111111, 0, 111211111111, 2111111111111, 0, 31111111111111, 212111111111111, 0, 1111111111111111111, 2111111111111111111, 0, 111111111111111121111, 11111111111111111111111, 0, 211111111111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Conjecture: a(n) = 0 only for n = 1 or n = 3k with k>1.
LINKS
EXAMPLE
a(4) = 211 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 211 is the largest prime using a partition.
MAPLE
with(combinat):
a:= proc(n) local k, w;
if n=1 or n>3 and irem(n, 3)=0 then return 0 fi;
for k from 0 do w:= max(select(isprime,
map(x-> parse(cat(x[])), [seq(permute(i)[],
i=map(x->[x[], 1$(n-k)], partition(k)))]))[]);
if w>0 then return w fi
od
end:
seq(a(n), n=1..30); # Alois P. Heinz, May 25 2013
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, Max@t, 0]] ]]; Array[f, 29]
CROSSREFS
Sequence in context: A157883 A038317 A157781 * A079841 A110782 A088073
KEYWORD
nonn,base
AUTHOR
Amarnath Murthy, Apr 21 2002
EXTENSIONS
More terms from David Wasserman, Apr 30 2003
a(8) corrected and a(16)-a(24) added by Robert G. Wilson v, Feb 06 2006
a(25) from Alois P. Heinz, May 25 2013
STATUS
approved

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Last modified September 23 16:20 EDT 2023. Contains 365554 sequences. (Running on oeis4.)