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A262989 Predestined numbers A262743 generated from at least a pair of products in which, for each product, all digits 0 through 9 are used, and each digit appears exactly once.

%I A262989 #24 Oct 10 2015 09:37:52
%S A262989 248665082,248695370,249063875,253674980,256175640,257930648,
%T A262989 257938064,260577504,260817480,263987504,264713960,267766632,
%U A262989 267953048,269037548,269045192,269174192,269307584,269735900,269937500
%N A262989 Predestined numbers A262743 generated from at least a pair of products in which, for each product, all digits 0 through 9 are used, and each digit appears exactly once.
%C A262989 Sequence obtained using the A050278 sequence of pandigitals numbers "over" the A262743 sequence of predestined numbers.
%C A262989 Pandigital numbers are numbers containing the digits 0 through 9 (in this case Version 1: each digit appears exactly once).
%C A262989 This is a finite sequence: first term is 248665082 (106*2345897 and 2378*104569) and last term is 8282993378 (853*9710426 and 8503*974126).
%C A262989 The sequence contains 95009 terms. - _Giovanni Resta_, Oct 07 2015
%D A262989 Francesco Di Matteo, Sequenze ludiche, Game Edizioni (2015), page 37.
%H A262989 Francesco Di Matteo, <a href="/A262989/b262989.txt">Table of n, a(n) for n = 1..19</a>
%H A262989 Andrea Marchini, <a href="/A262989/a262989.txt">The first 19 terms calculated</a>
%H A262989 Andrea Marchini, <a href="/A262989/a262989_1.txt">The last 23 terms calculated</a>
%H A262989 Andrea Marchini, <a href="/A262989/a262989_2.txt">All the 95009 terms with product pairs</a>, Oct 10 2015.
%e A262989 248665082 = 106*2345897 and 2378*104569;
%e A262989 248695370 = 10*24869537 and 1045*237986, 1045*237986 and 1*248695370;
%e A262989 249063875 = 2375*104869 and 1*249063875;
%e A262989 ...
%e A262989 8270423667 = 87*95062341 and 957*8642031;
%e A262989 8271362484 = 957*8643012 and 8526*970134;
%e A262989 8282993378 = 853*9710426 and 8503*974126.
%t A262989 good[w_]:=Block[{L={}}, Do[If[ Length[ Select[ Join[w[[i]], w[[j]]], Mod[#,10]==0&]]<=1,AppendTo[L, {w[[i]], w[[j]]}]], {i, Length@w}, {j, i-1}]; L]; f[w_]:=Select[ Table[ FromDigits/@ {Take[w, i], Take[w, i-10]}, {i, 5}], #[[1]] <= #[[2]] && IntegerLength[#[[1]]] + IntegerLength[ #[[2]]] == 10&]; p = Select[ Permutations@ Range[0, 9], First[#] > 0&]; t = SplitBy[ Sort[{ Times@@ #, #} &/@ Flatten[ f/@ p, 1]], First]; u = Select[ (Last/@ #) &/@ Select[t, Length[#] > 1&], good[#] != {} &]; seq = Union[ Times @@@ Flatten[u, 1]]; Length@ seq (* _Giovanni Resta_, Oct 07 2015 *)
%Y A262989 Cf. A050278, A262743.
%K A262989 nonn,base,fini
%O A262989 1,1
%A A262989 _Francesco Di Matteo_, Oct 06 2015