A072543 Numbers whose largest decimal digit is also the initial digit.

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

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