



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
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OFFSET

1,2


COMMENTS

Name was: Largest prime that is a concatenation of partitions of n; or 0 if no such number exists.
a(1) = a(3k+3)= 0. Conjecture: a(n) is nonzero for all other values of n.
When a repunit (10^n  1)/9 = A002275(n) is a repunit prime (A004022) then a(n) = A004022(n), as is the case for n = 2, 19, 23, 317, 1031, etcetera. See also: A000041 number of partitions of n (the partition numbers). For an a(n) = 0 one must have checked up to A000041 partitions for primality and chosen the maximum, or otherwise eliminated all possibilities by proof. E.g. a(9) = 0 as all integers in the partition must be single digits, whose sum must be 9, hence any such concatenation must be divisible by 9.  Jonathan Vos Post, Mar 20 2006


LINKS

Table of n, a(n) for n=1..25.


EXAMPLE

a(4) = 211 though 31 and 13 are also prime.


CROSSREFS

Cf. A000040, A000041, A004022, A002275.
Sequence in context: A038317 A157781 A069869 * A110782 A088073 A010187
Adjacent sequences: A079838 A079839 A079840 * A079842 A079843 A079844


KEYWORD

dead


AUTHOR

Amarnath Murthy, Feb 16 2003


EXTENSIONS

More terms from Jonathan Vos Post, Mar 20 2006


STATUS

approved



