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A256118 Nine-digit zeroless pandigital numbers that are concatenation of three 3-digit prime numbers in increasing order. 1

%I

%S 127463859,127643859,149257683,149257863,149263587,149263857,

%T 149563827,149653827,157463829,157643829,163457829,163547829,

%U 239461587,239461857,239587641,239641857,241367859,241673859,241769853,241853967,251389467

%N Nine-digit zeroless pandigital numbers that are concatenation of three 3-digit prime numbers in increasing order.

%C The sequence is finite with last term a(136) = 659743821.

%H Zak Seidov, <a href="/A256118/b256118.txt">Table of n, a(n) for n = 1..136</a>

%e (127, 463, 859) is the least triple of 3-digit primes together using each of nine digits 1..9 exactly once. Hence a(1) = 127463859.

%t fQ[n_] := Block[{d = DigitCount@ n}, And[Max@ d == 1, Last@ d == 0, Plus @@ d == 9, n == FromDigits@ Flatten[IntegerDigits /@ Select[FromDigits /@ Partition[IntegerDigits@ n, 3], PrimeQ]]]]; Select[FromDigits /@ DeleteDuplicates[Flatten /@ (Sort@ Partition[IntegerDigits@ #, 3] & /@ FromDigits /@ Permutations[Range@ 9])], fQ@ # &] (* _Michael De Vlieger_, Mar 15 2015 *)

%t pnioQ[n_]:=Module[{idn=Partition[n,3],a,b,c},{a,b,c}=FromDigits/@ idn; a<b<c && AllTrue[{a,b,c},PrimeQ]]; FromDigits/@ Select[ Permutations[ Range[ 9]], pnioQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Oct 18 2016 *)

%Y Cf. A050278, A115301 (3 primes unsorted).

%K nonn,base,fini,full

%O 1,1

%A _Zak Seidov_, Mar 15 2015

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Last modified April 21 23:52 EDT 2021. Contains 343156 sequences. (Running on oeis4.)