A102830 -id:A102830 - cp's OEIS frontend

A102823 "True already", base 10, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 0.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 56, 57, 58, 59, 60, 67, 68, 69, 70, 78, 79, 80, 89, 90, 100, 102, 103, 104, 105, 106, 107, 108, 109, 112, 113

Offset: 0

Hugo van der Sanden, Feb 26 2005

a(n) = A249626(n) for n <= 55. - Reinhard Zumkeller, Nov 03 2014

			The first 11 values of the sequence written in decimal include 2 '1's and 1 '2', so the next value cannot be 11 (the count of '1's is not 1) but can be 12.

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Cf. A102824-A102830, A102357.

Cf. A249626.

A102824 "True already", base 2, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 2 contains floor(a(n)/2) copies of the digit a(n) % 2, with a(0) = 0.

Original entry on oeis.org

0, 1, 2, 4, 7, 8, 14, 16, 23, 26, 30, 32, 42, 48, 56, 62, 64, 75, 82, 89, 96, 101, 109, 116, 122, 126, 128, 142, 150, 158, 164, 174, 180, 188, 194, 204, 212, 220, 226, 234, 240, 248, 254, 256, 272, 286, 294, 304, 316, 324, 336, 345, 355, 364, 372, 380, 386

Offset: 0

Hugo van der Sanden, Feb 26 2005

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Cf. A102823-A102830, A102357.

A102827 "True already", base 10, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 55, 56, 57, 58, 59, 66, 67, 68, 69, 77, 78, 79, 88, 89, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 123, 124, 125, 126, 127, 128, 129, 133

Offset: 0

Hugo van der Sanden, Feb 26 2005

Conjecture: this sequence in various bases never includes a term divisible by the base.

			The first 9 values of the sequence written in decimal include no '0's and 1 '1', so the next value cannot be 10 (the count of '0's is not 1) but can be 11.

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Cf. A102823-A102830, A102357.

A102827aux := proc(n,dig)
    local c,d ;
    c := 0 ;
    for d in convert(n,base,10) do
        if d = dig then
            c := c+1 ;
        end if;
    end do:
    c ;
end proc:
A102827 := proc(n)
    option remember;
    local a,a10,ad,cum;
    if n < 8 then
        return n+1 ;
    end if;
    for a from 1 do
        a10 := floor(a/10) ;
        ad := a mod 10 ;
        cum := add( A102827aux(procname(i),ad),i=0..n-1) ;
        if cum = a10 then
            return a;
        end if;
    end do:
end proc: # R. J. Mathar, Mar 30 2014

A102829 "True already", base 3, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 3 contains floor(a(n)/3) copies of the digit a(n) % 3, with a(0) = 1.

Original entry on oeis.org

1, 2, 4, 5, 8, 13, 14, 17, 23, 29, 32, 35, 41, 44, 50, 56, 62, 67, 74, 76, 82, 88, 92, 95, 98, 104, 110, 113, 116, 122, 125, 131, 137, 143, 152, 161, 173, 179, 188, 193, 202, 206, 215, 223, 226, 232, 238, 244, 250, 256, 263, 269, 274, 278, 284, 287, 293, 299

Offset: 0

Hugo van der Sanden, Feb 26 2005

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Cf. A102823-A102830, A102357.

A102825 "True already", base 3, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 3 contains floor(a(n)/3) copies of the digit a(n) % 3, with a(0) = 0.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 9, 11, 14, 17, 18, 24, 25, 27, 31, 38, 41, 42, 45, 50, 51, 54, 63, 68, 69, 72, 78, 81, 88, 94, 98, 104, 108, 110, 113, 116, 122, 125, 129, 132, 135, 143, 147, 150, 153, 159, 162, 174, 180, 188, 192, 198, 204, 207, 213, 216, 225, 231

Offset: 0

Hugo van der Sanden, Feb 26 2005

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Cf. A102823-A102830, A102357.

A102826 "True already", base 4, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 4 contains floor(a(n)/4) copies of the digit a(n) % 4, with a(0) = 0.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 7, 8, 11, 12, 16, 18, 19, 22, 23, 26, 27, 31, 32, 39, 40, 43, 44, 48, 55, 56, 60, 64, 69, 70, 74, 75, 79, 86, 87, 90, 91, 95, 96, 103, 104, 107, 108, 112, 119, 120, 124, 128, 138, 139, 143, 151, 152, 155, 156, 160, 163, 167, 171, 172, 176

Offset: 0

Hugo van der Sanden, Feb 26 2005

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Cf. A102823-A102830, A102357.

A102828 "True already", base 2, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 2 contains floor(a(n)/2) copies of the digit a(n) % 2, with a(0) = 1.

Original entry on oeis.org

1, 3, 7, 13, 19, 25, 31, 41, 47, 57, 65, 69, 75, 83, 91, 101, 109, 119, 131, 137, 143, 153, 161, 167, 177, 185, 195, 203, 213, 223, 237, 249, 261, 267, 275, 283, 293, 301, 311, 323, 331, 341, 351, 365, 377, 389, 397, 407, 419, 429, 441, 453, 463, 477, 491

Offset: 0

Hugo van der Sanden, Feb 26 2005

Inspired by discussion of "True so far" from Eric Angelini (A102357).

Cf. A102823-A102830, A102357.

cp's OEIS Frontend

A102823 "True already", base 10, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 0.

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A102824 "True already", base 2, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 2 contains floor(a(n)/2) copies of the digit a(n) % 2, with a(0) = 0.

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A102827 "True already", base 10, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 1.

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A102829 "True already", base 3, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 3 contains floor(a(n)/3) copies of the digit a(n) % 3, with a(0) = 1.

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A102825 "True already", base 3, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 3 contains floor(a(n)/3) copies of the digit a(n) % 3, with a(0) = 0.

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A102826 "True already", base 4, start 0: a(n) is the least integer such that the sequence up to a(n-1) written in base 4 contains floor(a(n)/4) copies of the digit a(n) % 4, with a(0) = 0.

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A102828 "True already", base 2, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 2 contains floor(a(n)/2) copies of the digit a(n) % 2, with a(0) = 1.

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