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A072543 Numbers whose largest decimal digit is also the initial digit. 4
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 20, 21, 22, 30, 31, 32, 33, 40, 41, 42, 43, 44, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 66, 70, 71, 72, 73, 74, 75, 76, 77, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 110, 111, 200, 201 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A054055(a(n)) = A000030(a(n));

the sequence differs from A009996, A032873 and A032907: a(66)=101 is not in A009996, a(67)=110 is not in A032873 and a(65)=100 is not in A032907.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

EXAMPLE

a(10^ 1) = 9

a(10^ 2) = 411

a(10^ 3) = 6216

a(10^ 4) = 73474

a(10^ 5) = 813826

a(10^ 6) = 8512170

a(10^ 7) = 88368780

a(10^ 8) = 911960211

a(10^ 9) = 9237655227

a(10^10) = 93323313303

MAPLE

for i from 1 to 10 do A[i]:= i-1 od:

count:= 10:

for i from 1 to 9 do P[i]:= [seq([j], j=0..i)]; od:

for d from 2 to 4 do

  for x from 1 to 9 do

    for p in P[x] do

      count:= count+1;

      A[count]:= add(p[k]*10^(k-1), k=1..d-1) + x*10^(d-1);

    od:

    P[x]:= [seq(seq([op(v), t], v=P[x]), t=0..x)];

  od

od:

seq(A[i], i=1..count); # Robert Israel, Feb 01 2015

MATHEMATICA

Select[Range[0, 250], Max[IntegerDigits[#]]==First[IntegerDigits[#]]&] (* Harvey P. Dale, Apr 28 2016 *)

PROG

(Haskell)

a072543 n = a072543_list !! (n-1)

a072543_list = [x | x <- [0..], a054055 x == a000030 x]

-- Reinhard Zumkeller, Apr 25 2012

(PARI) is(n)=n=digits(n); !#n || n[1]==vecmax(n) \\ Charles R Greathouse IV, Jan 02 2014

(PARI) a(n)={d = 0; r = 1; s = 0; i = 0; if(n == 1, 0, n-=2; while(n > sum(i=0, 9, (i+1)^d), n-=sum(i=0, 9, (i+1)^d); n++; d++); while(n >= (r+1)^d, n -= (r+1)^d; r++); s = r * 10^d; while(n, s += 10^i*(n%(r+1)); n \= (r+1); i++)); s } \\ David A. Corneth, Jan 31 2015

CROSSREFS

Cf. A072544.

Sequence in context: A247754 A084383 A032873 * A009996 A032907 A130576

Adjacent sequences:  A072540 A072541 A072542 * A072544 A072545 A072546

KEYWORD

nonn,base,easy

AUTHOR

Reinhard Zumkeller, Aug 04 2002

EXTENSIONS

Offset corrected by Reinhard Zumkeller, Apr 25 2012

STATUS

approved

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Last modified October 18 03:34 EDT 2018. Contains 316304 sequences. (Running on oeis4.)