A007376 -id:A007376 - cp's OEIS frontend

A127950 a(n) = A007376(8*n+2).

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

Offset: 0

N. J. A. Sloane, Jul 23 2008

G. C. Greubel, Table of n, a(n) for n = 0..10000

Cf. A007376.

A007376 := Flatten[IntegerDigits /@ Range[1600]]; Table[A007376[[8*n + 2]], {n, 0, 100}] (* G. C. Greubel, May 05 2018 *)

from itertools import islice, count
def A127950gen(): return islice((int(d) for n in count(0) for d in str(n)),2,None,8)
A127950_list = list(islice(A127950gen(),40)) # Chai Wah Wu, Dec 04 2021

A128475 A007376(8n+7).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Jul 23 2008

A254649 a(1) = A007376(1) = 1, n > 1: a(n) = smallest number not occurring earlier, that is the sum of unused next consecutive terms of A007376.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 19, 14, 13, 17, 12, 16, 18, 20, 21, 22, 26, 25, 31, 30, 28, 27, 36, 33, 43, 24, 39, 29, 32, 34, 35, 23, 45, 41, 40, 37, 44, 46, 38, 47, 48, 51, 52, 50, 57, 58, 42, 59, 55, 53, 60, 49, 56, 54, 61, 63, 65, 62, 64, 66, 72

Offset: 1

Reinhard Zumkeller, Feb 04 2015

nonn

A permutation of the positive integers with inverse A254650.

			.     n |1|2|3|4|5|6|7|8|9|10             |11     |12     |13     |14
.  a(n) |1|2|3|4|5|6|7|8|9|           10  |    11 |    15 |    19 |     14
--------+-+-+-+-+-+-+-+-+-+---------------+-------+-------+-------+--------
A007376 |1|2|3|4|5|6|7|8|9|1+0+1+1+1+2+1+3|1+4+1+5|1+6+1+7|1+8+1+9|2+0+2....
-

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A007376, A033307, A254650 (inverse), A254656 (fixed points).

a254649 n = a254649_list !! (n-1)
a254649_list = f a007376_list [0] where
   f (x:xs) ys = g x xs where
     g y zs'@(z:zs) | y `elem` ys = g (y + z) zs
                    | otherwise   = y : f zs' (y:ys)

A098728 Consider the sequence {b(n), n >= 1} of digits of the natural (or counting) numbers: 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0... (A007376); a(n) = n - b(n).

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 11, 11, 12, 13, 13, 15, 14, 17, 15, 19, 16, 21, 17, 23, 18, 25, 19, 27, 20, 28, 31, 30, 32, 32, 33, 34, 34, 36, 35, 38, 36, 40, 37, 42, 38, 44, 39, 46, 40, 47, 51, 49, 52, 51, 53, 53, 54, 55, 55, 57, 56, 59, 57, 61, 58, 63, 59, 65, 60, 66, 71, 68, 72

Offset: 0

Alexandre Wajnberg, Sep 30 2004

Subtract each digit of the counting numbers from its rank.

			The sequence of digits of the counting numbers is
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0...
The 15th term, for instance, is a 2. Thus 15-2=13 is the 15th term of this sequence.
Next one is a 1, thus 16 (the rank) - 1 (the 16th digit of the decimal expansion of the counting numbers) = 15, which is the 16th term of this sequence.
Next one is 17-3=14

Harvey P. Dale, Table of n, a(n) for n = 0..1000

With[{c=Flatten[IntegerDigits/@Range[70]]},#[[1]]-#[[2]]&/@Partition[ Riffle[ Range[Length[c]],c],2]] (* Harvey P. Dale, Aug 07 2019 *)

More terms from Stacy Hawthorne (shawtho1(AT)ashland.edu), Jan 12 2006

A119385 Write out the digits of the integers in order (cf. A007376): 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 ...; a(n) = sum of digits between successive zeros.

Original entry on oeis.org

0, 46, 56, 66, 76, 86, 96, 106, 116, 126, 127, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 66, 76, 86, 96, 106, 116, 126, 136, 137, 0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 76, 86, 96, 106, 116, 126, 136, 146, 147, 0, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 86, 96, 106, 116, 126, 136, 146, 156, 157, 0, 4

Offset: 0

N. J. A. Sloane, Jul 26 2006

a(0) = 0 by convention.

c:=proc(x,y) local s: s:=proc(m) nops(convert(m,base,10)) end: if y=0 then 10*x else x*10^s(y)+y: fi end: b:=proc(n) local nn: nn:=convert(n,base,10): [seq(nn[nops(nn)+1-i],i=1..nops(nn))] end: A:=0: for n from 1 to 500 do A:=c(A,n) od: B:=[0,seq(b(A)[j],j=1..nops(b(A)))]: u:=proc(n) if B[n]=0 then n else fi end: U:=[seq(u(n),n=1..nops(B))]: 0,seq(add(B[j],j=U[i]..U[i+1]),i=1..nops(U)-1); # there must exist a simpler Maple program! - Emeric Deutsch, Jul 27 2006
#alternative
A119385 := proc(n) option remember ; local nupto,a,a007376,k ; if n =0 then RETURN([0,0]) ; else nupto := op(2,A119385(n-1)) ; a := 0 ; for k from nupto+1 do a007376 := A007376(k) ; if op(1,a007376) > 0 then a := a+op(1,a007376) ; else RETURN([a,k]) ; fi ; od: fi ; end :# R. J. Mathar, Jan 21 2008

list1=Flatten[Table[IntegerDigits[i],{i,0,1000}]];
index1=Partition[Flatten[Position[list1,0]],2,1];
Plus@@@Table[Take[list1,Flatten[Take[index1,{i}]]],{i,Length[index1]}] (From Harvey Dale)

More terms from Emeric Deutsch, Jul 27 2006

A127414 a(n) = A007376(4*n+1).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Jul 23 2008

A007376=Flatten[ IntegerDigits/@Range@ 500] ;Array[A007376[[4#+1]]&,105,0] (* James C. McMahon, Dec 31 2024 *)

A127508 A007376(4n+2).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Jul 23 2008

A127584 A007376(4n+3).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Jul 23 2008

A127734 A007376(4n).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Jul 23 2008

A127794 A007376(8n+1).

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Jul 23 2008

cp's OEIS Frontend

A127950 a(n) = A007376(8*n+2).

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A128475 A007376(8n+7).

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A254649 a(1) = A007376(1) = 1, n > 1: a(n) = smallest number not occurring earlier, that is the sum of unused next consecutive terms of A007376.

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Haskell

A098728 Consider the sequence {b(n), n >= 1} of digits of the natural (or counting) numbers: 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 2 0... (A007376); a(n) = n - b(n).

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Mathematica

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A119385 Write out the digits of the integers in order (cf. A007376): 0 1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 ...; a(n) = sum of digits between successive zeros.

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Maple

Mathematica

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A127414 a(n) = A007376(4*n+1).

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Mathematica

A127508 A007376(4n+2).

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A127584 A007376(4n+3).

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A127734 A007376(4n).

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A127794 A007376(8n+1).

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