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.

10234567889, 100223456789, 100234566789, 100234567889, 101234556789, 101234567789, 102234456789, 102234566789, 102334556789, 102334567899, 102344456789, 102344567889, 102345567789, 102345666789, 102345677789, 102345678899, 1000223456789, 1000234456789, 1000234566789

Offset: 1

Author

Robert Israel and Altug Alkan, Sep 06 2016

Keywords

• nonn
• base

Comments

The least pandigital number in A276510 is 10234567889.

Each member of the sequence has digits in increasing order except that the first digit is 1.

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.

Examples

			100223456789 is a term because A045876(100223456789) = 52113599999947886400 is pandigital.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1557

Crossrefs

Cf. A045876, A171102, A276510.

Programs

Maple

pandig:= n -> evalb(nops(convert(convert(n,base,10),set))=10):
sump:= proc(x) local L, D, n, M, s, j;
  L:= convert(x, base, 10);
  D:= [seq(numboccur(j, L), j=0..9)];
  n:= nops(L);
  M:= n!/mul(d!, d=D);
  s:= add(j*D[j+1], j=0..9);
  (10^n-1)*M/9/n*s
end proc:
n0:= 1023456789:
rep:= proc(n) local L,n0,i;
  L:= sort(convert(n,base, 10));
  n0:= numboccur(0, L);
  L:= subsop(1=1,n0+1=0,L);
  add(L[-i-1]*10^(i),i=0..nops(L)-1); end proc:
sort(convert(map(rep,
select(pandig @ sump, {seq(seq(n0*10^d+x,x=0..10^d-1),d=0..3)})),list));