A140301 Numbers k whose digits contain, in any substring of consecutive digits, the number of digits of k (ND) and the sum of digits of k (SD). Common digits for ND and SD are admitted while cycling is not.

1, 20, 139, 300, 913, 1045, 1054, 1145, 1148, 1154, 1245, 1254, 1345, 1354, 1409, 1418, 1427, 1436, 1445, 1454, 1463, 1472, 1481, 1490, 1545, 1554, 1645, 1654, 1745, 1754, 1814, 1845, 1854, 1945, 1954, 2147, 2499, 2714, 3146, 3614, 4000, 4105, 4115

Offset

0,2

Links

Table of n, a(n) for n=0..42.

Example

k=1 -> ND(k)=1; SD(k)=1.
k=20 -> ND(k)=2; SD(k)=2.
k=139 -> ND(k)=3 (second digit); SD(k)=13 (first and second digits).
k=300 -> ND(k)=3; SD(k)=3.
k=913 -> ND(k)=3 (third digit); SD(k)=13 (second and third digits).
k=1045 -> ND(k)=4 (third digit); SD(k)=10 (first and second digits).
etc.

Maple

P:=proc(n) local i, j, k, ok, w, x, t1, t2; for i from 1 by 1 to n do j:=trunc(1+evalf(log10(i))); w:=0; k:=i; ok:=0; while k>0 do x:=k-(trunc(k/10)*10); if x=j then ok:=1; fi; w:=w+x; k:=trunc(k/10); od; if ok=1 then t1:=convert(w, string); t2:=convert(i, string); if searchtext(t1, t2)>0 then print(i); fi; fi; od; end: P(10000);

Crossrefs

Sequence in context: A105573 A144965 A262140 * A264315 A264308 A328174

Adjacent sequences: A140298 A140299 A140300 * A140302 A140303 A140304

Keyword

easy,nonn,base

Author

Paolo P. Lava and Giorgio Balzarotti, May 27 2008

Status

approved