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A284591 “Full Inside numbers”. Such numbers have the property that all their digits will be visited exactly once in a single closed circuit (see Comments). 5
100, 1102, 11122, 30000, 111124, 130200, 300102, 330004, 1031202, 1111144, 1132200, 1302102, 1332004, 3001122, 3031024, 3102120, 3130240, 3300142, 3330044, 3332222, 5000000, 5011222, 5112220, 5310242, 5312024, 10110140, 10312122, 11031402, 11111146, 11132400, 11322102, 11332006, 13021122, 13031026, 13122120, 13130440 (list; graph; refs; listen; history; text; internal format)



The sequence is started with a(1) = 100 and always extended with the smallest integer not yet present and not leading to a contradiction. See A284515 for the definition of an “Inside number”. Listed in the b-file are the 544 first “Full Inside numbers”.


Lars Blomberg, Table of n, a(n) for n = 1..10000 (The first 544 terms from Jean-Marc Falcoz)


The 13th term of the sequence is 1332004. This integer is in the sequence because starting on the first digit “1”, will lead to the second “3” (after jumping over exactly one digit to the right), then to “4” (after jumping exactly over three digits to the right), then to the first “3” (after jumping exactly over four digits to the left), then to the last “0” (after jumping exactly over three digits to the right), then to the first “0” (after jumping exactly over no digit to the left, which is equivalent to “sliding” to the digit on the left), then to “2” (same reason), then to the initial “1” (after jumping exactly over two digits to the left. The cycle has come to its end. (The direction -left or right- of a jump is given by the parity -odd or even- of the digit involved.)


P:=proc(q) local a, b, j, k, ok, n; for n from 100 to q do a:=trunc(n/10^ilog10(n)); if a mod 2=0 then n:=(a+1)*10^ilog10(n)-1;

else a:=[]; b:=n; for k from 1 to ilog10(n)+1 do a:=[b mod 10, op(a)]; b:=trunc(b/10); od; b:=array(1..ilog10(n)+1); k:=1; ok:=1;

for j from 1 to nops(a) do if a[k] mod 2=1 then k:=k+a[k]+1;

else k:=k-a[k]-1; fi; if k>nops(a) or k<1 then ok:=0; break;

else if b[k]<>0 then b[k]:=0; else ok:=0; break; fi; fi; od;

if ok=1 then print(n); fi; fi; od; end: P(10^9); # Paolo P. Lava, Mar 30 2017


Cf. A284515, A284591, A285471, A285695, A285696

Sequence in context: A124166 A103175 A163450 * A129725 A167043 A274943

Adjacent sequences:  A284588 A284589 A284590 * A284592 A284593 A284594




Eric Angelini and Jean-Marc Falcoz, Mar 29 2017 and Mar 30 2017



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Last modified September 27 03:21 EDT 2020. Contains 337380 sequences. (Running on oeis4.)