A104759
Concatenation of digits of natural numbers from n down to 1.
Original entry on oeis.org
1, 21, 321, 4321, 54321, 654321, 7654321, 87654321, 987654321, 1987654321, 1987654321, 101987654321, 1101987654321, 11101987654321, 211101987654321, 1211101987654321, 31211101987654321, 131211101987654321, 4131211101987654321, 14131211101987654321, 514131211101987654321
Offset: 1
a(11) = a(10) because no number may begin with 0.
a(9)= [123456789]101112131415...=987654321
a(10)=[1234567891]01112131415...=1987654321
a(11)=[12345678910]1112131415...=01987654321=1987654321
a(12)=[123456789101]112131415...=101987654321
a(13)=[1234567891011]12131415...=1101987654321
a(14)=[12345678910111]2131415...=11101987654321
a(15)=[123456789101112]131415...=211101987654321
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f[n_] := Block[{t = Reverse@ Flatten@ IntegerDigits@ Range@ n, k}, Reap@ For[k = 1, k <= Length@ t, k++, Sow[FromDigits@ Take[t, -k]]] // Flatten // Rest]; f@ 14 (* Michael De Vlieger, Mar 23 2015 *)
lst = {}; Do[lst = Join[lst, IntegerDigits[n]], {n, 1, 100}]; Table[FromDigits[Reverse[lst[[Range[1, n]]]]], {n, 1, Length[lst]}] (* Robert Price, Mar 24 2015 *)
A057137
Concatenate next digit at right hand end (where the next digit after 9 is again 0).
Original entry on oeis.org
0, 1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 1234567890, 12345678901, 123456789012, 1234567890123, 12345678901234, 123456789012345, 1234567890123456, 12345678901234567, 123456789012345678, 1234567890123456789, 12345678901234567890, 123456789012345678901
Offset: 0
- Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61.
- T. D. Noe and Hieronymus Fischer, Table of n, a(n) for n = 0..200 (terms up to 100 from T. D. Noe)
- Clifford Pickover, Triangle of the Gods
- Index entries for linear recurrences with constant coefficients, signature (10,0,0,0,0,0,0,0,0,1,-10).
Alternative progression for n >= 10 compared with
A007908 and
A014824.
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A057137:=n->floor((137174210/1111111111)*10^n); seq(A057137(n), n=0..20); # Wesley Ivan Hurt, Apr 18 2014
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a[n_]:=Floor[137174210/1111111111*10^n]; Array[a,19,0] (* Robert G. Wilson v, Apr 18 2014 *)
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A057137(n)=sum(i=1,n,i%10*10^(n-i)) \\ M. F. Hasler, Jan 13 2013
-
A057137(n)=137174210*10^n\1111111111 \\ M. F. Hasler, Jan 13 2013
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def A057137(n): s = '0123456789'; return int((n+1)//10*s + s[:(n+1)%10]) # Ya-Ping Lu, Apr 08 2025
A057139
Odd number of digits palindrome based on sequential digits.
Original entry on oeis.org
1, 121, 12321, 1234321, 123454321, 12345654321, 1234567654321, 123456787654321, 12345678987654321, 1234567890987654321, 123456789010987654321, 12345678901210987654321, 1234567890123210987654321, 123456789012343210987654321, 12345678901234543210987654321
Offset: 1
Alternative progression for n >= 10 compared with
A002477.
-
Array[FromDigits@ Join[#, Reverse@ Most@ #] &@ Mod[Range[#], 10] &, 15] (* Michael De Vlieger, Jan 28 2020 *)
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a(n)={fromdigits(vector(2*n-1, i, if(i<=n, i, 2*n-i)%10))} \\ Andrew Howroyd, Jan 27 2020
A137233
Number of n-digit even numbers.
Original entry on oeis.org
5, 45, 450, 4500, 45000, 450000, 4500000, 45000000, 450000000, 4500000000, 45000000000, 450000000000, 4500000000000, 45000000000000, 450000000000000, 4500000000000000, 45000000000000000, 450000000000000000, 4500000000000000000, 45000000000000000000, 450000000000000000000
Offset: 1
a(2) = 45 because there are 45 2-digit even numbers.
Cf.
A000422,
A002275,
A002276,
A011577,
A014923,
A014925,
A016313,
A019518,
A037487,
A053052,
A057138,
A090843,
A097166,
A099914,
A099915.
Showing 1-4 of 4 results.
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