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A276590 Pandigital numbers n such that sum of all permutations of digits of n is also a pandigital number. Sequence lists the least ones of corresponding permutational classes.

%I A276590 #24 Sep 17 2016 00:16:53
%S A276590 10234567889,100223456789,100234566789,100234567889,101234556789,
%T A276590 101234567789,102234456789,102234566789,102334556789,102334567899,
%U A276590 102344456789,102344567889,102345567789,102345666789,102345677789,102345678899,1000223456789,1000234456789,1000234566789
%N A276590 Pandigital numbers n such that sum of all permutations of digits of n is also a pandigital number. Sequence lists the least ones of corresponding permutational classes.
%C A276590 The least pandigital number in A276510 is 10234567889.
%C A276590 Each member of the sequence has digits in increasing order except that the first digit is 1.
%C A276590 The sequence has 1 member with 11 digits, 15 with 12 digits, 90 with 13 digits, 261 with 14 digits and 1190 with 15 digits.
%H A276590 Robert Israel, <a href="/A276590/b276590.txt">Table of n, a(n) for n = 1..1557</a>
%e A276590 100223456789 is a term because A045876(100223456789) = 52113599999947886400 is pandigital.
%p A276590 pandig:= n -> evalb(nops(convert(convert(n,base,10),set))=10):
%p A276590 sump:= proc(x) local L, D, n, M, s, j;
%p A276590   L:= convert(x, base, 10);
%p A276590   D:= [seq(numboccur(j, L), j=0..9)];
%p A276590   n:= nops(L);
%p A276590   M:= n!/mul(d!, d=D);
%p A276590   s:= add(j*D[j+1], j=0..9);
%p A276590   (10^n-1)*M/9/n*s
%p A276590 end proc:
%p A276590 n0:= 1023456789:
%p A276590 rep:= proc(n) local L,n0,i;
%p A276590   L:= sort(convert(n,base, 10));
%p A276590   n0:= numboccur(0, L);
%p A276590   L:= subsop(1=1,n0+1=0,L);
%p A276590   add(L[-i-1]*10^(i),i=0..nops(L)-1); end proc:
%p A276590 sort(convert(map(rep,
%p A276590 select(pandig @ sump, {seq(seq(n0*10^d+x,x=0..10^d-1),d=0..3)})),list));
%Y A276590 Cf. A045876, A171102, A276510.
%K A276590 nonn,base
%O A276590 1,1
%A A276590 _Robert Israel_ and _Altug Alkan_, Sep 06 2016