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A087555
a(n) = largest prime that is the concatenation of two numbers whose sum is n.
3
11, 0, 31, 41, 0, 61, 71, 0, 73, 101, 0, 211, 311, 0, 313, 107, 0, 811, 911, 0, 211, 1013, 0, 1213, 1511, 0, 1117, 1811, 0, 2011, 2111, 0, 2311, 2411, 0, 2017, 2711, 0, 2713, 3011, 0, 2617, 431, 0, 3511, 3413, 0, 3613, 3911, 0, 4111, 4211, 0, 541, 3917, 0, 4513, 4217
OFFSET
2,1
COMMENTS
a(3k) = 0. Conjecture: No other term is zero.
Conjecture is false: first counterexample is 4477. See A375938. - Robert Israel, Sep 03 2024
LINKS
EXAMPLE
a(10) = 73, the partitions of 10 are (1,9), (2,8), (3,7), (4,6), (5,5) and the primes obtained are 19,37 and 73.
MAPLE
f:= proc(n) local L, a, x;
if n mod 3 = 0 then return 0 fi;
L:= sort([seq(tcat(n-a, a), a=1..n-1, 2)], `>`);
for x in L do if isprime(x) then return x fi od;
0
end proc:
map(f, [$2..100]); # Robert Israel, Sep 03 2024
MATHEMATICA
lpc[n_]:=Max[Select[FromDigits[Flatten[IntegerDigits[#]]]&/@(Flatten[{#, Reverse[#]}&/@ IntegerPartitions[ n, {2}], 1]), PrimeQ]]; Array[lpc, 60, 2]/.(-\[Infinity])->0 (* Harvey P. Dale, Aug 02 2024 *)
CROSSREFS
Sequence in context: A075360 A256756 A087558 * A185682 A217752 A335646
KEYWORD
base,nonn,look
AUTHOR
Amarnath Murthy, Sep 13 2003
EXTENSIONS
More terms from David Wasserman, Jun 07 2005
STATUS
approved