A000030 Initial digit of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

N. J. A. Sloane, Simon Plouffe

Keywords

• nonn
• base
• easy
• nice
• look
• changed

Comments

When n - a(n)*10^[log_10 n] >= 10^[(log_10 n) - 1], where [] denotes floor, or when n < 100 and 10|n, n is the concatenation of a(n) and A217657(n). - Reinhard Zumkeller, Oct 10 2012, improved by M. F. Hasler, Nov 17 2018, and corrected by Glen Whitney, Jul 01 2022

Equivalent definition: The initial a(0) = 0 is followed by each digit in S = {1,...,9} once. Thereafter, repeat 10 times each digit in S. Then, repeat 100 times each digit in S, etc.

Examples

			23 begins with a 2, so a(23) = 2.
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• David W. Wilson, Table of n, a(n) for n = 0..10000
• A. Cobham, Uniform Tag Sequences, Mathematical Systems Theory, 6 (1972), 164-192.

Crossrefs

Cf. A010879 (final digit of n).

Cf. A061681, A130571, A109453, A134010, A052038.

Cf. A002993, A089951, A002994, A143464, A098174, A098175, A072543, A072544, A073600, A073601, A037904. - Reinhard Zumkeller, Aug 17 2008

Programs

Haskell

a000030 = until (< 10) (`div` 10) -- Reinhard Zumkeller, Feb 20 2012, Feb 11 2011

Magma

[Intseq(n)[#Intseq(n)]: n in [1..100]]; // Vincenzo Librandi, Nov 17 2018

Maple

A000030 := proc(n)
    if n = 0 then
        0;
    else
        convert(n,base,10) ;
        %[-1] ;
    end if;
end proc:
seq(A000030(n),n=0..200) ;# N. J. A. Sloane, Feb 10 2017

Mathematica

Join[{0},First[IntegerDigits[#]]&/@Range[90]] (* Harvey P. Dale, Mar 01 2011 *)
Table[Floor[n/10^(Floor[Log10[n]])], {n, 1, 50}] (* G. C. Greubel, May 16 2017 *)
Table[NumberDigit[n,IntegerLength[n]-1],{n,0,100}] (* Harvey P. Dale, Aug 29 2021 *)

PARI

a(n)=if(n<10,n,a(n\10)) \\ Mainly for illustration.

PARI

A000030(n)=n\10^logint(n+!n,10) \\ Twice as fast as a(n)=digits(n)[1]. Before digits() was added in PARI v.2.6.0 (2013), one could use, e.g., Vecsmall(Str(n))[1]-48. - M. F. Hasler, Nov 17 2018

Python

def a(n): return int(str(n)[0])
print([a(n) for n in range(85)]) # Michael S. Branicky, Jul 01 2022

Formula

a(n) = [n / 10^([log_10(n)])] where [] denotes floor and log_10(n) is the logarithm is base 10. - Dan Fux (dan.fux(AT)OpenGaia.com or danfux(AT)OpenGaia.com), Apr 07 2001

a(n) = k for k*10^j <= n < (k+1)*10^j for some j. - M. F. Hasler, Mar 23 2015