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.

A167523 Positions of zero digits in A167503 (when all terms are concatenated).

Original entry on oeis.org

4, 8, 12, 13, 15, 18, 30, 33, 37, 46, 54, 55, 56, 58, 59, 62, 63, 66, 70, 74, 78, 83, 84, 87, 92, 104, 115, 116, 119, 124, 136, 146, 148, 150, 152, 154, 159, 163, 176, 183, 184, 187, 192, 210, 211, 212, 213, 215, 216, 217, 220, 221, 225, 226, 230, 231, 235, 236, 240
Offset: 1

Views

Author

M. F. Hasler, Nov 05 2009

Keywords

Comments

Also, positive integers not occurring in A167503 (bearing in mind that the terms of A167503 are written in base 3, but here numbers are written in base 10).

Examples

			Sequence A167503: 1,2,10,12,20,21,100,101
Digit's position: 1 2 34 56 78 9A BCD EFG (A=10,...)
Thus the digits '0' occur at positions 4,8,12,13,15,...: this sequence.

Crossrefs

Cf. A167500-A167503.

Programs

  • PARI
    base(n,b=3,s=1) = { my( a=[ n%b ]); while( 0=n && for(i=a[n-1]+1,#b,b[i] && (a=concat(a,i)) && break); #a

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

A167519 Lexicographically earliest increasing sequence which lists the positions of the zero digits in the sequence.

Original entry on oeis.org

3, 10, 11, 12, 11000, 11111, 11112, 11113, 11114, 11115, 11116, 11117, 11118, 11119, 11121, 11122, 11123, 11124, 11125, 11126, 11127, 11128, 11129, 11131, 11132, 11133, 11134, 11135, 11136, 11137, 11138, 11139, 11141, 11142, 11143, 11144
Offset: 1

Views

Author

M. F. Hasler, Nov 05 2009

Keywords

Comments

The terms of the sequence give the positions of the digits '0' in the string formed by concatenating all the terms (written in base 10).

Examples

			The sequence cannot start with 1 (which would mean it starts with 0) or 2 (which would mean that the second term equals 0), so a(1)=3 is the smallest possibility.
Thereafter, the smallest possible value for a(2), which must have '0' as second digit, is a(2)=10.
This means that the next digit '0' must occur at position 10; up to there, we use the smallest possible values for a(3)=11 and a(4)=12.
Then must follow two nonzero digits (which must be part of a(5)) and then three zero digits (from a(2),a(3),a(4) = 10, 11, 12). None of the latter can be the first digit of a(6), so they must be part of a(5), for which the smallest possibility is therefore a(5)=11000.
This also means that there is no digit '0' between the 12th digit (= the last digit of a(6)), and the 11000th digit of the sequence. So there follow roughly 11000/5 terms which are the smallest possible 5-digit terms without a zero digit.

Crossrefs

Cf. A167500-A167503. See A210414 for another version.

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010
Definition corrected by Jaroslav Krizek, Jun 19 2014

A167521 Positive integers not occurring in A167520.

Original entry on oeis.org

11, 29, 47, 67, 85, 105, 123, 143, 161, 181, 182, 184, 187, 190, 193, 196, 199, 202, 205, 209, 239, 266, 296, 323, 353, 380, 410, 445, 446, 448, 451, 454, 457, 460, 463, 467, 497, 527, 554, 584, 614, 641, 671, 701, 727, 728, 730, 733, 736, 739, 742, 745, 748
Offset: 1

Views

Author

M. F. Hasler, Nov 05 2009

Keywords

Comments

Equivalently, positions of zero digits in A167520 (when all terms are concatenated).
The first differences are (18, 18, 20, 18, 20, 18, 20, 18, 20, 1, 2, 3, 3, 3, 3, 3, 3, 3, 4, 30, 27, 30, 27, 30, 27, 30, 35, 1, 2, 3, 3, 3, 3, 3, 4, ...)

Examples

			The first occurrence of the digit '0' in A167520 is as the least significant digit of A167520(10)=10, which occurs at position 11, thus a(1)=11. Equivalently, this is the least positive integer missing in A167520.
The next occurrence of the digit '0' in A167520 is at position 29 (and 29 is the second positive integer not occurring in A167520), thus a(2)=29.

Crossrefs

Cf. A167500-A167503, A167520-A167523.

Programs

  • PARI
    base(n,b=10) = { my( a=[ n%b ]); while( 0=n & for(i=a[n-1]+1,#b,b[i] & (a=concat(a,i)) & break); #a

A167522 Positive integers not occurring in A167500.

Original entry on oeis.org

3, 5, 6, 11, 12, 13, 15, 16, 19, 21, 25, 27, 28, 29, 32, 33, 35, 37, 39, 40, 42, 45, 47, 53, 54, 55, 58, 60, 65, 72, 73, 74, 76, 78, 79, 81, 82, 84, 85, 88, 90, 92, 93, 96, 98, 102, 105, 106, 108, 112, 115, 116, 117, 118, 121, 122, 123, 127, 128, 130, 133, 134, 139, 141
Offset: 1

Views

Author

M. F. Hasler, Nov 05 2009

Keywords

Comments

Equivalently, positions of zero digits in A167502 (when all terms are concatenated).

Crossrefs

Cf. A167500-A167503, A167520-A167523.

Programs

  • PARI
    {a=b=[]; for(n=1,99, #b>=n & for(i=a[n-1]+1,#b,b[i] & (a=concat(a,i)) & break); #a
Showing 1-4 of 4 results.

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