A054637 -id:A054637 - cp's OEIS frontend

A055073 Positions in A054635 where the partial sums (A054637) yield primes (A055072).

3, 6, 8, 10, 11, 12, 16, 17, 18, 30, 32, 37, 40, 41, 43, 44, 45, 55, 57, 68, 74, 75, 76, 84, 85, 94, 95, 101, 106, 113, 128, 131, 136, 138, 149, 154, 159, 171, 172, 178, 179, 180, 181, 182, 183, 184, 212, 214, 226, 228, 229, 240, 241, 245, 258, 259, 260, 275, 278

Offset: 1

Patrick De Geest, Apr 15 2000

			012101112202122100101102110111112120121122200201...
--|..... sum 0+1+2 = prime 3 at position 3
-----|.. sum 0+1+2+1+0+1 = prime 5 at position 6
-------| sum 0+1+2+1+0+1+1+1 = prime 7 at position 8

Cf. A054635, A054637, A055072.

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

A055072 Primes in A054637.

Original entry on oeis.org

3, 5, 7, 11, 13, 19, 29, 31, 37, 41, 43, 47, 59, 61, 79, 83, 89, 97, 103, 109, 113, 127, 131, 137, 139, 151, 157, 163, 179, 181, 191, 193, 223, 227, 239, 241, 257, 263, 281, 283, 307, 311, 313, 331, 337, 347, 349, 353, 367, 373, 383, 397, 409, 419, 433, 439

Offset: 1

Patrick De Geest, Apr 15 2000

			012101112202122100101102110111112120121122200201...
--|..... sum 0+1+2 = prime 3
-----|.. sum 0+1+2+1+0+1 = prime 5
-------| sum 0+1+2+1+0+1+1+1 = prime 7

Cf. A054637, A055073, A055059-A055074.

Offset changed by Georg Fischer, Sep 02 2022

A054635 Champernowne sequence: write n in base 3 and juxtapose.

Original entry on oeis.org

0, 1, 2, 1, 0, 1, 1, 1, 2, 2, 0, 2, 1, 2, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 1, 0, 2, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1

Offset: 0

N. J. A. Sloane, Apr 16 2000

Essentially the same as A003137. - R. J. Mathar, Aug 29 2009
An irregular table in which the n-th row lists the base-3 digits of n. - Jason Kimberley, Dec 07 2012
The base-3 Champernowne constant (A077771): it is normal in base 3. - Jason Kimberley, Dec 07 2012

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened
Eric Weisstein's World of Mathematics, Ternary Champernowne Constant
Wikipedia, Ternary numeral system

Cf. A054637 (partial sums).
Cf. A081604 (row lengths), A053735 (row sums), A030341 (rows reversed), A007089, A077771.
Table in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and this sequence (b=3), A030373 (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and A054634 (b=8), A031076 (b=9), A007376 and A033307 (b=10). - Jason Kimberley, Dec 06 2012

a054635 n k = a054635_tabf !! n !! k
a054635_row n = a054635_tabf !! n
a054635_tabf = map reverse a030341_tabf
a054635_list = concat a054635_tabf
-- Reinhard Zumkeller, Feb 21 2013

[0]cat &cat[Reverse(IntegerToSequence(n,3)):n in[1..31]]; // Jason Kimberley, Dec 07 2012

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[#, 3] &, 105, 0] (* Robert G. Wilson v, Jun 29 2014 *)
First[RealDigits[ChampernowneNumber[3], 3, 100, 0]] (* Paolo Xausa, Jun 19 2024 *)

from sympy.ntheory.digits import digits
def agen(limit):
    for n in range(limit):
        yield from digits(n, 3)[1:]
print([an for an in agen(35)]) # Michael S. Branicky, Sep 01 2021

A055144 The first n digits of the juxtaposition of the base-3 numbers converted to decimal.

Original entry on oeis.org

1, 5, 16, 48, 145, 436, 1309, 3929, 11789, 35367, 106103, 318310, 954932, 2864798, 8594395, 25783185, 77349555, 232048666, 696145998, 2088437995, 6265313986, 18795941958, 56387825876, 169163477629, 507490432888, 1522471298664

Offset: 1

Patrick De Geest, Apr 15 2000

			1 (1); 12 (5); 121 (16); 1210 (48); 12101 (145); 121011 (436); ...

Cf. A054635, A054637, A055072, A055073, A055143-A055150.

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A055073 Positions in A054635 where the partial sums (A054637) yield primes (A055072).

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A055072 Primes in A054637.

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A054635 Champernowne sequence: write n in base 3 and juxtapose.

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A055144 The first n digits of the juxtaposition of the base-3 numbers converted to decimal.

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