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.

248665082, 248695370, 249063875, 253674980, 256175640, 257930648, 257938064, 260577504, 260817480, 263987504, 264713960, 267766632, 267953048, 269037548, 269045192, 269174192, 269307584, 269735900, 269937500

Offset: 1

Author

Francesco Di Matteo, Oct 06 2015

Keywords

• nonn
• base
• fini

Comments

Sequence obtained using the A050278 sequence of pandigitals numbers "over" the A262743 sequence of predestined numbers.

Pandigital numbers are numbers containing the digits 0 through 9 (in this case Version 1: each digit appears exactly once).

This is a finite sequence: first term is 248665082 (106*2345897 and 2378*104569) and last term is 8282993378 (853*9710426 and 8503*974126).

The sequence contains 95009 terms. - Giovanni Resta, Oct 07 2015

Examples

			248665082 = 106*2345897 and 2378*104569;
248695370 = 10*24869537 and 1045*237986, 1045*237986 and 1*248695370;
249063875 = 2375*104869 and 1*249063875;
...
8270423667 = 87*95062341 and 957*8642031;
8271362484 = 957*8643012 and 8526*970134;
8282993378 = 853*9710426 and 8503*974126.
		

References

• Francesco Di Matteo, Sequenze ludiche, Game Edizioni (2015), page 37.

Links

• Francesco Di Matteo, Table of n, a(n) for n = 1..19
• Andrea Marchini, The first 19 terms calculated
• Andrea Marchini, The last 23 terms calculated
• Andrea Marchini, All the 95009 terms with product pairs, Oct 10 2015.

Crossrefs

Cf. A050278, A262743.

Programs

Mathematica

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 *)