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.

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A284800 Fixed points of the transform A284799.

Original entry on oeis.org

6, 9, 12, 78, 90, 102, 114, 141, 153, 165, 177, 204, 216, 228, 240, 1086, 1134, 1182, 1230, 1338, 1386, 1434, 1482, 1590, 1638, 1686, 1734, 1842, 1890, 1938, 1986, 2109, 2157, 2205, 2253, 2361, 2409, 2457, 2505, 2613, 2661, 2709, 2757, 2865, 2913, 2961, 3009, 3132
Offset: 1

Views

Author

Paolo P. Lava, Apr 03 2017

Keywords

Comments

All terms are divisible by 3. - Robert Israel, Apr 01 2020

Examples

			78 is a term of the sequence because 78 in base 4 is 1032, its complement in base 4 is 2301 and the digit reverse is again 1032 that is 78 in base 10.

Links

Crossrefs

Cf. A035928, A284799.

Programs

  • Maple
    P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;
for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,4);

A284811 Fixed points of the transform A267193.

Original entry on oeis.org

18, 27, 36, 45, 54, 63, 72, 81, 90, 1098, 1188, 1278, 1368, 1458, 1548, 1638, 1728, 1818, 1908, 2097, 2187, 2277, 2367, 2457, 2547, 2637, 2727, 2817, 2907, 3096, 3186, 3276, 3366, 3456, 3546, 3636, 3726, 3816, 3906, 4095, 4185, 4275, 4365, 4455, 4545, 4635, 4725
Offset: 1

Views

Author

Paolo P. Lava, Apr 05 2017

Keywords

Comments

These numbers are called antipalindromic in base 10 by Dvorakova et al. - Michel Marcus, Aug 18 2020

Examples

			1278 is a term of the sequence because its complement in base 10 is 8721 and the digit reversal is again 1278.

Links

Crossrefs

Cf. A035928, A061601, A267193.
Subsequence of A008591 (multiples of 9).

Programs

  • Maple
    P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;
for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,10);
  • PARI
    isok(m) = {my(d=digits(m)); for (j=1, #d, if (d[j] + d[#d+1-j] != 9, return(0));); return (1);} \\ Michel Marcus, Aug 18 2020
  • PARI
    a(n) = my (d=digits(n)); n*10^#d + fromdigits(apply (t -> 9-t, Vecrev(d))) \\ Rémy Sigrist, Aug 18 2020

A351176 Natural numbers k such that k = A/B has at least one solution in antipalindromic numbers A, B, but only finitely many solutions.

Original entry on oeis.org

5, 17, 21, 26, 65, 69, 70, 85, 89, 92, 102, 106, 116, 219, 221, 233, 239, 245, 249, 257, 261, 269, 273, 276, 284, 290, 291, 294, 301, 306, 307, 319, 323, 324, 333, 341, 344, 356, 361, 364, 369, 392, 398, 426, 434, 460, 468, 488, 843, 869, 879, 919, 925, 971
Offset: 1

Views

Author

Jeffrey Shallit, Feb 04 2022

Keywords

Comments

"Antipalindromic" means a member of A035928.
This sequence and A351175 form a disjoint partition of A351172.

Links

Crossrefs

Cf. A035928, A351172, A351175.

A284802 Fixed points of the transform A284801.

Original entry on oeis.org

2, 8, 12, 16, 20, 38, 62, 86, 110, 148, 168, 188, 208, 228, 272, 292, 312, 332, 352, 396, 416, 436, 456, 476, 520, 540, 560, 580, 600, 698, 818, 938, 1058, 1178, 1322, 1442, 1562, 1682, 1802, 1946, 2066, 2186, 2306, 2426, 2570, 2690, 2810, 2930, 3050, 3248, 3348
Offset: 1

Views

Author

Paolo P. Lava, Apr 03 2017

Keywords

Examples

			86 is a term of the sequence because 86 in base 5 is 321, its complement in base 5 is 123 and the digit reverse is again 321 that is 86 in base 10.

Crossrefs

Cf. A035928, A284801.

Programs

  • Maple
    P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;
for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,5);

A284804 Fixed points of the transform A284803.

Original entry on oeis.org

10, 15, 20, 25, 30, 250, 280, 310, 340, 370, 400, 465, 495, 525, 555, 585, 615, 680, 710, 740, 770, 800, 830, 895, 925, 955, 985, 1015, 1045, 1110, 1140, 1170, 1200, 1230, 1260, 7990, 8170, 8350, 8530, 8710, 8890, 9280, 9460, 9640, 9820, 10000, 10180, 10570, 10750
Offset: 1

Views

Author

Paolo P. Lava, Apr 03 2017

Keywords

Examples

			310 is a term of the sequence because 310 in base 6 is 1234, its complement in base 3 is 4321 and the digit reverse is again 1234 that is 310 in base 10.

Crossrefs

Cf. A035928, A284803.

Programs

  • Maple
    P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;
for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,6);

A284806 Fixed points of the transform A284805.

Original entry on oeis.org

3, 12, 18, 24, 30, 36, 42, 75, 123, 171, 219, 267, 315, 390, 432, 474, 516, 558, 600, 642, 732, 774, 816, 858, 900, 942, 984, 1074, 1116, 1158, 1200, 1242, 1284, 1326, 1416, 1458, 1500, 1542, 1584, 1626, 1668, 1758, 1800, 1842, 1884, 1926, 1968, 2010, 2100, 2142
Offset: 1

Views

Author

Paolo P. Lava, Apr 03 2017

Keywords

Examples

			219 is a term of the sequence because 219 in base 7 is 432, its complement in base 7 is 234 and the digit reverse is again 432 that is 219 in base 10.

Crossrefs

Cf. A035928, A284805.

Programs

  • Maple
    P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;
for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,7);

A284808 Fixed points of the transform A284807.

Original entry on oeis.org

14, 21, 28, 35, 42, 49, 56, 574, 630, 686, 742, 798, 854, 910, 966, 1085, 1141, 1197, 1253, 1309, 1365, 1421, 1477, 1596, 1652, 1708, 1764, 1820, 1876, 1932, 1988, 2107, 2163, 2219, 2275, 2331, 2387, 2443, 2499, 2618, 2674, 2730, 2786, 2842, 2898, 2954, 3010, 3129
Offset: 1

Views

Author

Paolo P. Lava, Apr 03 2017

Keywords

Examples

			966 is a term of the sequence because 966 in base 8 is 1706, its complement in base 8 is 6071 and the digit reverse is again 1706 that is 966 in base 10.

Crossrefs

Cf. A035928, A284807.

Programs

  • Maple
    P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;
for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,8);

A284810 Fixed points of the transform A284809.

Original entry on oeis.org

4, 16, 24, 32, 40, 48, 56, 64, 72, 124, 204, 284, 364, 444, 524, 604, 684, 808, 880, 952, 1024, 1096, 1168, 1240, 1312, 1384, 1536, 1608, 1680, 1752, 1824, 1896, 1968, 2040, 2112, 2264, 2336, 2408, 2480, 2552, 2624, 2696, 2768, 2840, 2992, 3064, 3136, 3208, 3280
Offset: 1

Views

Author

Paolo P. Lava, Apr 04 2017

Keywords

Examples

			952 is a term of the sequence because 952 in base 9 is 1267, its complement in base 9 is 7621 and the digit reverse is again 1267 that is 952 in base 10.

Crossrefs

Cf. A035928, A284809.

Programs

  • Maple
    P:=proc(q,h) local a,b,k,n; for n from 1 to q do a:=convert(n,base,h); b:=0;
for k from 1 to nops(a) do a[k]:=h-1-a[k]; b:=h*b+a[k]; od; if b=n then print(n); fi; od; end: P(10^2,9);

A051242 Array T by antidiagonals; T(n,k)=k-th binary number d(1),...,d(j) for which exactly n digits d(i) satisfy d(i)=d(j+1-i) (n=0,1,2,...; k=1,2,3,..).

Original entry on oeis.org

2, 10, 1, 12, 4, 3, 38, 6, 8, 5, 42, 18, 11, 7, 9, 52, 22, 13, 16, 15, 17, 56, 24, 14, 19, 32, 21, 33, 142, 28, 34, 20, 35, 27, 45, 65, 150, 70, 36, 23, 37, 31, 51, 73, 129, 170, 78, 39, 25, 41, 64, 63, 85, 153, 257, 178, 82, 40, 26, 44, 67, 128
Offset: 1

Views

Author

Clark Kimberling

Keywords

Examples

			Antidiagonals: {2}; {10,1}; {12,4,3}; ...
Top row: {2,10,12,38,42,...}=A035928.

A066489 Binary expansion of n followed by its reverse complement.

Original entry on oeis.org

10, 1010, 1100, 100110, 101010, 110100, 111000, 10001110, 10010110, 10101010, 10110010, 11001100, 11010100, 11101000, 11110000, 1000011110, 1000101110, 1001010110, 1001100110, 1010011010, 1010101010, 1011010010, 1011100010, 1100011100, 1100101100, 1101010100
Offset: 1

Views

Author

John McNamara, Jan 09 2002

Keywords

Examples

			a(2) = 1010 because 2 in binary is 10, the complement of which is 01, the reverse of which is 10, hence (10)(10). - _Sean A. Irvine_, Oct 22 2023

Crossrefs

Binary expansion of numbers in A035928.

Programs

  • Maple
    a:= n-> (l-> parse(cat(seq(l[-i], i=1..nops(l)), 1-~l[])))(Bits[Split](n)):
seq(a(n), n=1..30);  # Alois P. Heinz, Oct 22 2023
  • PARI
    a(n)={my(v=binary(n)); fromdigits(concat(v,vector(#v,i,1-v[#v+1-i])))} \\ Andrew Howroyd, Oct 22 2023

Extensions

Title clarified and more terms from Sean A. Irvine, Oct 22 2023
Previous Showing 21-30 of 33 results. Next

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