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

Author

Reinhard Zumkeller, Aug 04 2002

Keywords

• nonn
• base
• easy

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A072544.

Programs

Haskell

a072543 n = a072543_list !! (n-1)
a072543_list = [x | x <- [0..], a054055 x == a000030 x]
-- Reinhard Zumkeller, Apr 25 2012

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 *)

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

Extensions

Offset corrected by Reinhard Zumkeller, Apr 25 2012