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A171725 6-digit numbers k such that: (a) the digits of k are from the set {1, 2, 3, 4, 5}, and (b) any digit that appears in k appears at least twice. 2
111111, 111122, 111133, 111144, 111155, 111212, 111221, 111222, 111313, 111331, 111333, 111414, 111441, 111444, 111515, 111551, 111555, 112112, 112121, 112122, 112211, 112212, 112221, 112222, 112233, 112244, 112255, 112323, 112332, 112424, 112442, 112525, 112552 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See Problem 4 of RMO 2007 (Regional Mathematical Olympiad-India).

There are exactly 1405 such numbers from 111111, 111122,... to ..., 555544, 555555.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..1405 (full sequence)

|nSan|ty, RMO 2007 problem

MAPLE

A171725:={}: for n from 9331 to 46655 do d:=convert(n, base, 6): for k from 0 to 5 do cordig:=true: if((k=0 and numboccur(k, d)>0) or (k>0 and numboccur(k, d)=1))then cordig:=false:break: fi: od: if(cordig)then A171725 := A171725 union {op(convert(d, base, 10, 10^nops(d)))}: fi: od: op(sort(convert(A171725, list))); # Nathaniel Johnston, Jun 24 2011

MATHEMATICA

cc=0; re=Reap[Do[dc=DigitCount[n]; If[Take[dc, {6, 10}]=={0, 0, 0, 0, 0}&&FreeQ[Take[dc, 5], 1], cc++; Sow[n]], {n, 111111, 555555}]][[2, 1]]; cc

CROSSREFS

Sequence in context: A205243 A223110 A094325 * A135403 A154549 A038448

Adjacent sequences:  A171722 A171723 A171724 * A171726 A171727 A171728

KEYWORD

base,fini,full,nonn

AUTHOR

Zak Seidov, Dec 16 2009

STATUS

approved

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Last modified July 30 23:12 EDT 2021. Contains 346365 sequences. (Running on oeis4.)