A052038 -id:A052038 - cp's OEIS frontend

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

N. J. A. Sloane, Simon Plouffe

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.

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

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

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

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

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

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

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

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 *)

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

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

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

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

A052039 a(n) is the smallest k such that the first significant digits of 1/k coincide with n.

Original entry on oeis.org

1, 4, 3, 21, 2, 15, 13, 12, 11, 91, 9, 8, 72, 7, 63, 6, 56, 53, 51, 48, 46, 44, 42, 41, 4, 38, 36, 35, 34, 33, 32, 31, 3, 29, 28, 271, 27, 26, 251, 244, 24, 233, 23, 223, 22, 213, 21, 205, 201, 197, 193, 19, 186, 182, 18, 176, 173, 17, 167, 164, 162, 16, 157, 154, 152

Offset: 1

Patrick De Geest, Dec 15 1999

This sequence differs from A326818 in how it treats reciprocals with terminating representation, i.e., the values 1/k for integers k whose prime factors are 2 and/or 5. For example, in A326818 we assume 1/5 = 0.2000... which leads to A326818(20) = 5, while here we consider 1/5 = 0.2 (without trailing zeros), which leads to a(20) = 48 instead. - Giovanni Resta, Oct 20 2019

			a(36) = 271 because 1/271 = 0.00{36}9003690036900... and 271 is the smallest number with this property.

Cf. A052038, A326818.

dinv[x_, m_] := Block[{t = If[1 == x/ 2^IntegerExponent[x,2]/ 5^IntegerExponent[x,5], RealDigits[1/x], RealDigits[1/x, 10, m]][[1]]}, If[ Length[t] > m, Take[t, m], t]]; a[n_] := Block[{d = IntegerDigits[n], m, k = 1}, m = Length[d]; While[dinv[k, m] != d, k++]; k]; Array[a, 65] (* Giovanni Resta, Oct 20 2019 *)

A061861 First two significant digits of 1/n written in decimal.

Original entry on oeis.org

10, 50, 33, 25, 20, 16, 14, 12, 11, 10, 90, 83, 76, 71, 66, 62, 58, 55, 52, 50, 47, 45, 43, 41, 40, 38, 37, 35, 34, 33, 32, 31, 30, 29, 28, 27, 27, 26, 25, 25, 24, 23, 23, 22, 22, 21, 21, 20, 20, 20, 19, 19, 18, 18, 18, 17, 17, 17, 16, 16, 16, 16, 15, 15, 15, 15, 14, 14, 14

Offset: 1

Henry Bottomley, May 11 2001

After 10^k terms the number of times m will have appeared will be about 10^(k+2)/(9*m*(m+1)); e.g., 10 will appear just over 10.1% of the time.

			a(32)=31 since 1/32 = 0.0312500000...

Cf. A033420, A033421, A052038.

Table[FromDigits[RealDigits[1/n,10,2][[1]]],{n,70}] (* Harvey P. Dale, Jan 19 2018 *)

a(n) = floor(10^floor(2+log_10(n-1))/n).

A353179 a(n) is the first nonzero digit in the decimal expansion of 1/prime(n).

Original entry on oeis.org

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

Offset: 1

Firdous Ahmad Mala, Apr 29 2022

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A052038, A000040.

a:= n-> (p-> floor(10^length(p)/p))(ithprime(n)):
seq(a(n), n=1..100);  # Alois P. Heinz, Apr 30 2022

Table[RealDigits[1/Prime[n],10,1][[1]],{n,100}]//Flatten (* Harvey P. Dale, Aug 25 2024 *)

a(n) = my(p=prime(n)); floor(10^(1+logint(p-1, 10))/p) \\ Felix Fröhlich, Apr 29 2022

a(n) = A052038(prime(n)).

More terms from Felix Fröhlich, Apr 29 2022

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A000030 Initial digit of n.

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A052039 a(n) is the smallest k such that the first significant digits of 1/k coincide with n.

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A061861 First two significant digits of 1/n written in decimal.

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A353179 a(n) is the first nonzero digit in the decimal expansion of 1/prime(n).

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