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A262989
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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.
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1
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248665082, 248695370, 249063875, 253674980, 256175640, 257930648, 257938064, 260577504, 260817480, 263987504, 264713960, 267766632, 267953048, 269037548, 269045192, 269174192, 269307584, 269735900, 269937500
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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).
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REFERENCES
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Francesco Di Matteo, Sequenze ludiche, Game Edizioni (2015), page 37.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,base,fini
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AUTHOR
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STATUS
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approved
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