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 1-3 of 3 results.

A032841 Numbers whose base-3 representation Sum_{i=0..m} d(i)*3^i has d(m) < d(m-1) > d(m-2) < ...

Original entry on oeis.org

1, 2, 5, 15, 16, 46, 47, 50, 138, 141, 142, 150, 151, 415, 416, 424, 425, 428, 451, 452, 455, 1245, 1248, 1249, 1272, 1275, 1276, 1284, 1285, 1353, 1356, 1357, 1365, 1366, 3736, 3737, 3745, 3746, 3749, 3817, 3818, 3826, 3827
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

For any a(n) == 0 (mod 3), 3*a(n)+1 and 3*a(n)+2 are also in the sequence, but 3*a(n) is not. Likewise, for any a(n) == 2 (mod 3) -- except for a(2)=2 -- 3*a(n) and 3*a(n)+1 are in the sequence but 3*a(n)+2 is not. - Christian N. K. Anderson, May 21 2024

Examples

			The numbers {415, 416, 424, 425, 428, 451, 452, 455} are in the sequence because in base 3 they are {120101, 120102, 120201, 120202, 120212, 121201, 121202, 121212}; all the six-digit base-3 numbers that fit the pattern. - _Christian N. K. Anderson_, May 21 2024

Links

Crossrefs

Cf. A032850 for digits <= or >= previous digit (also in base 3).
Cf. A032842 for same sequence in base 4, A032843 base 5, A032844 base 6, A032845 base 7, A032846 base 8, A032847 base 9, A032848 base 10, and A032849 base 2.

Programs

  • R
    updown.base<-function(base,ndig,curdig=1,diglist=rep(NA,ndig)) {
if(curdig>ndig) return(sum(base^(ndig:1-1)*diglist)); nextstep<-function(i) {diglist[curdig]=i; updown.base(base,ndig,curdig+1,diglist)}; if(curdig==1) return(sort(unlist(sapply(1:(base-2+(ndig==1)), nextstep)))); if(curdig%%2) return(sapply((diglist[curdig-1]-1):0, nextstep)); sapply((diglist[curdig-1]+1):(base-1), nextstep) }; sapply(1:10,function(nd) updown.base(3,nd)) # Christian N. K. Anderson, May 21 2024

A032842 Numbers whose base-4 representation Sum_{i=0..m} d(i)*4^i has d(m) < d(m-1) > d(m-2) < ...

Original entry on oeis.org

1, 2, 3, 6, 7, 11, 24, 25, 28, 29, 30, 44, 45, 46, 97, 98, 99, 102, 103, 113, 114, 115, 118, 119, 123, 177, 178, 179, 182, 183, 187, 388, 392, 393, 396, 397, 398, 408, 409, 412, 413, 414, 452, 456, 457, 460, 461, 462, 472, 473, 476
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

For any term a(n) == 0 (mod 4), the three terms 4*a(n)+{1,2,3} are also in {a(n)}. If a(n) == 3 (mod 4), except for a(3)=3, then 4*a(n)+{0,1,2} are in the sequence. - Christian N. K. Anderson, May 24 2024

Examples

			The numbers {24, 25, 28, 29, 30, 44, 45, 46} are in the sequence because in base-4 they are {120, 121, 130, 131, 132, 230, 231, 232}, i.e., all the three-digit base-4 numbers that fit the pattern. - _Christian N. K. Anderson_, May 24 2024

Links

Crossrefs

Cf. A032851 for digits <= or >= previous digit (also in base 4).
Cf. A032841 for same sequence in base 3 (with program), A032843 base 5, A032844 base 6, A032845 base 7, A032846 base 8, A032847 base 9, A032848 base 10, and A032849 base 2.

A032904 Numbers whose base-7 representation Sum_{i=0..m} d(i)*7^i has d(0) <= d(1) >= d(2) <= ...

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 14, 15, 16, 21, 22, 23, 24, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 56, 57, 63, 64, 65, 70, 71, 72, 73, 77, 78, 79, 80, 81, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 112, 113, 114, 119, 120, 121, 122, 126, 127
Offset: 1

Views

Author

Clark Kimberling

Keywords

Examples

			a(36)=63 since 63 = 49 + 7 + 7 is written 120 in base 7 and 0 <= 2 >= 1.

Crossrefs

Cf. A023763.
Cf. A032845, A032854, A032870, A032886, A032895, A032904.

Extensions

Corrected by Henry Bottomley, Jul 03 2000
Showing 1-3 of 3 results.

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