cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A055059 Positions in A007376 where the partial sums (A054632) yield primes (A055058).

Original entry on oeis.org

3, 13, 21, 23, 24, 35, 36, 42, 45, 61, 83, 85, 114, 115, 135, 141, 149, 181, 200, 201, 203, 204, 212, 213, 215, 216, 234, 237, 239, 242, 247, 251, 260, 263, 272, 285, 292, 297, 309, 311, 332, 335, 347, 350, 357, 359, 371, 392, 396, 405, 410, 417, 419, 431
Offset: 1

Views

Author

Patrick De Geest, Apr 15 2000

Keywords

Examples

			0123456789101112131415161718192021...
--|.................. sum 0+1+2 = prime 3 at position 3
------------|........ sum 0+1+2+3+4+5+6+7+8+9+1+0+1 = prime 47 at position 13
--------------------| sum 0+1+2+3+4+5+6+7+8+9+1+0+1+1+1+2+1+3+1+4+1 = prime 61 at position 21

Crossrefs

Cf. A007376, A054632, A055058.

Extensions

Definition amended and offset changed by Georg Fischer, Sep 03 2022

A055058 Primes in A054632.

Original entry on oeis.org

3, 47, 61, 67, 73, 107, 109, 127, 137, 193, 283, 293, 433, 439, 547, 577, 631, 829, 907, 911, 929, 937, 971, 977, 983, 991, 1009, 1021, 1033, 1039, 1063, 1103, 1117, 1129, 1171, 1181, 1237, 1249, 1289, 1297, 1321, 1327, 1381, 1451, 1471, 1511, 1523, 1553
Offset: 1

Views

Author

Patrick De Geest, Apr 15 2000

Keywords

Examples

			0123456789101112131415161718192021...
--|.................. sum 0+1+2 = prime 3
------------|........ sum 0+1+2+3+4+5+6+7+8+9+1+0+1 = prime 47
--------------------| sum 0+1+2+3+4+5+6+7+8+9+1+0+1+1+1+2+1+3+1+4+1 = prime 61

Crossrefs

Cf. A054632, A055059.

Extensions

Offset changed by Georg Fischer, Sep 02 2022

A007376 The almost-natural numbers: write n in base 10 and juxtapose digits.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

Comments

Also called the Barbier infinite word.
This is an example of a non-morphic sequence.
a(n) = A162711(n,1); A136414(n) = 10*a(n) + a(n+1). - Reinhard Zumkeller, Jul 11 2009
a(A031287(n)) = 0, a(A031288(n)) = 1, a(A031289(n)) = 2, a(A031290(n)) = 3, a(A031291(n)) = 4, a(A031292(n)) = 5, a(A031293(n)) = 6, a(A031294(n)) = 7, a(A031295(n)) = 8, a(A031296(n)) = 9. - Reinhard Zumkeller, Jul 28 2011
May be regarded as an irregular table in which the n-th row lists the digits of n. - Jason Kimberley, Dec 07 2012
The digits of the integer n start at index A117804(n). The digit a(n) at index n belongs to the number A100470(n). - M. F. Hasler, Oct 23 2019
See also the Copeland-Erdős constant A033308, equivalent using primes instead of all numbers. - M. F. Hasler, Oct 24 2019
Decimal expansion of Sum_{k>=1} k/10^(A058183(k) + 1). - Stefano Spezia, Nov 30 2022

References

  • J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, pp. 114, 336.
  • R. Honsberger, Mathematical Chestnuts from Around the World, MAA, 2001; see p. 163.
  • M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
  • David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, p. 26.

Links

Crossrefs

Considered as a sequence of digits, this is the same as the decimal expansion of the Champernowne constant, A033307. See that entry for a formula for a(n), further references, etc.
Cf. A054632 (partial sums), A023103.
For "decimations" see A127050 A127353 A127414 A127508 A127584 A127734 A127794 A127950 A128178 A128211 A128359 A128423 A128475 A128881.
Cf. A193428, A256100, A001477 (the nonnegative integers), A117804, A100470.
Tables in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and A054635 (b=3), A030373 (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and A054634 (b=8), A031076 (b=9), this sequence and A033307 (b=10). - Jason Kimberley, Dec 06 2012
Row lengths in A055642.
For primes here see A071620. See A007908 for a very similar sequence.
Cf. A031287, A031288, A031289, A031290, A031291, A031292, A031293, A031294, A031295, A031296, A033308, A058183, A136414, A162711.

Programs

  • Haskell
    a007376 n = a007376_list !! (n-1)
a007376_list = concatMap (map (read . return) . show) [0..] :: [Int]
-- Reinhard Zumkeller, Nov 11 2013, Dec 17 2011, Mar 28 2011
  • Magma
    &cat[Reverse(IntegerToSequence(n)):n in[0..31]]; // Jason Kimberley, Dec 07 2012
  • Maple
    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 75 do A:=c(A,n) od: b(A); # c concatenates 2 numbers while b converts a number to the sequence of its digits - Emeric Deutsch, Jul 27 2006
#alternative
A007376 := proc(n) option remember ; local aprev, dOld,N ; if n <=9 then RETURN([n,n,1]) ; else aprev := A007376(n-1) ; dOld := op(3,aprev) ; N := op(2,aprev) ; if dOld < A055642(N) then RETURN([op(-dOld-1,convert(N,base,10)),N,dOld+1]) ; else RETURN([op(-1,convert(N+1,base,10)),N+1,1]) ; fi ; fi ; end: # R. J. Mathar, Jan 21 2008
  • Mathematica
    Flatten[ IntegerDigits /@ Range@ 57] (* Or *)
almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; Array[ almostNatural[#, 10] &, 105] (* updated Jun 29 2014 *)
With[{nn=120},RealDigits[N[ChampernowneNumber[],nn],10,nn]][[1]] (* Harvey P. Dale, Mar 13 2018 *)
  • PARI
    for(n=0,90,v=digits(n);for(i=1,#v,print1(v[i]", "))) \\ Charles R Greathouse IV, Nov 20 2012
  • PARI
    apply( A007376(n)={for(k=1,n, k*10^k>n&& return(digits(n\k)[n%k+1]); n+=10^k)}, [0..200]) \\ M. F. Hasler, Nov 03 2019
  • Python
    A007376_list = [int(d) for n in range(10**2) for d in str(n)] # Chai Wah Wu, Feb 04 2015

Extensions

Extended to a(0) = 0 by M. F. Hasler, Oct 23 2019

A055062 Primes in A054636.

Original entry on oeis.org

3, 29, 31, 43, 71, 73, 101, 173, 179, 199, 251, 281, 307, 379, 409, 421, 449, 463, 487, 491, 499, 521, 541, 547, 571, 593, 599, 619, 641, 659, 701, 709, 727, 739, 809, 829, 877, 907, 919, 953, 967, 971, 997, 1009, 1013, 1019, 1031, 1039, 1049, 1069, 1097
Offset: 1

Views

Author

Patrick De Geest, Apr 15 2000

Keywords

Examples

			012345671011121314151617202122232425...
--|...... sum 0+1+2 = prime 3
--------| sum 0+1+2+3+4+5+6+7+1 = prime 29

Crossrefs

Cf. A055063, A055058, A054632, A054636.

Extensions

Offset changed by Georg Fischer, Sep 02 2022
Showing 1-4 of 4 results.

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