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.

Previous Showing 11-19 of 19 results.

A066127 Numbers that in base 2 need six 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

275, 301, 317, 361, 377, 401, 523, 579, 587, 603, 619, 637, 761, 777, 833, 841, 857, 873, 1043, 1063, 1091, 1107, 1179, 1197, 1213, 1227, 1261, 1277, 1293, 1295, 1315, 1413, 1415, 1437, 1439, 1449, 1465, 1485, 1487, 1513, 1529, 1553, 1555, 1573
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065211 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 6. - Andrew Howroyd, Dec 05 2024

Crossrefs

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 01 2010

A066128 Numbers that in base 2 need seven 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

326, 366, 452, 492, 644, 654, 692, 710, 718, 734, 750, 826, 882, 902, 908, 926, 942, 964, 972, 974, 982, 988, 990, 998, 1004, 1006, 1058, 1068, 1110, 1166, 1188, 1246, 1320, 1332, 1340, 1362, 1380, 1388, 1418, 1440, 1460, 1498, 1502, 1508, 1568
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065212 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 7. - Andrew Howroyd, Dec 05 2024

Crossrefs

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 01 2010

A066129 Numbers that in base 2 need eight 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

259, 285, 309, 345, 369, 385, 399, 423, 459, 479, 483, 503, 531, 547, 563, 653, 655, 709, 711, 785, 801, 817, 909, 919, 935, 959, 965, 1015, 1031, 1037, 1051, 1053, 1099, 1101, 1157, 1171, 1173, 1219, 1221, 1243, 1283, 1289, 1305, 1353, 1409, 1423
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065213 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 8. - Andrew Howroyd, Dec 05 2024

Crossrefs

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 01 2010

A066130 Numbers that in base 2 need nine 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

202, 210, 218, 222, 250, 282, 306, 312, 334, 358, 408, 432, 454, 460, 484, 778, 834, 842, 846, 858, 862, 874, 878, 970, 986, 1002, 1080, 1128, 1182, 1200, 1230, 1248, 1292, 1316, 1412, 1434, 1482, 1692, 1740, 1944, 1992, 2162, 2274, 2582, 2684, 2694
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065214 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 9. - Andrew Howroyd, Dec 05 2024

Crossrefs

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 01 2010

A066131 Numbers that in base 2 need ten 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

103, 115, 137, 145, 159, 187, 221, 249, 391, 407, 411, 435, 451, 467, 525, 581, 649, 705, 719, 733, 735, 749, 751, 973, 989, 1005, 1151, 1165, 1245, 1271, 1403, 1417, 1497, 1523, 1661, 1781, 1913, 2033, 2059, 2083, 2097, 2115, 2129, 2147, 2209, 2241
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065215 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 10. - Andrew Howroyd, Dec 05 2024

Crossrefs

A066132 Numbers that in base 2 need eleven 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

74, 104, 188, 298, 424, 494, 600, 616, 1276, 1286, 1454, 1470, 1518, 1528, 1786, 1790, 1796, 1964, 1980, 2028, 2042, 2144, 2552, 2556, 2564, 2566, 2598, 2622, 2630, 2654, 2662, 2676, 2686, 2734, 2766, 2788, 2798, 2870, 2902, 2934, 2982, 3014, 3046
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065216 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 11. - Andrew Howroyd, Dec 05 2024

Crossrefs

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 01 2010

A066133 Numbers that in base 2 need twelve 'Reverse and Add' steps to reach a palindrome.

Original entry on oeis.org

1027, 1139, 1181, 1229, 1433, 1481, 1537, 1649, 1951, 1983, 1999, 2031, 2051, 3073, 3103, 3215, 3351, 3463, 3611, 3639, 3671, 3723, 3751, 3783, 3839, 3859, 3971, 4087, 4103, 4121, 4141, 4187, 4237, 4269, 4327, 4331, 4333, 4361, 4427, 4603, 4625, 4645
Offset: 1

Views

Author

Klaus Brockhaus, Dec 08 2001

Keywords

Comments

The analog of A065217 in base 2. The number of steps starts at 0, so palindromes (cf. A006995) are excluded.
Numbers k such that A066057(k) = 12. - Andrew Howroyd, Dec 05 2024

Crossrefs

Programs

  • PARI
    isok(n,s=12)={for(k=0, s, my(r=fromdigits(Vecrev(binary(n)),2)); if(r==n, return(k==s)); n += r); 0} \\ Andrew Howroyd, Dec 05 2024

Extensions

Offset changed from 0 to 1 by Harry J. Smith, Feb 01 2010

A077402 Reverse and Add! carried out in base 3; number of steps needed to reach a palindrome, or -1 if no palindrome is ever reached.

Original entry on oeis.org

0, 0, 0, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 0, 2, 3, 0, 4, 1, 2, 0, 1, 2, 0, 3, 4, 0, 1, 0, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 0, 2, 3, 3, 2, 1, 1, 2, 3, 3, 2, 3, 0, 18, 1, 2, 0, 1, 2, 4, 1, 2, 2, 1, 2, 4, 1, 2, 0, 3, 2, 4, 1, 2, 2, 3, 2, 4, 17, 18, 0, 1, 0, 2, 1, 1, 2, 1, 1, 3, 1, 0, 2, 1, 1, 16, 1, 1, 2, 2, 0, 2, 4, -1, 16, 3, 15, 2, 1, 1, 2, 1, 0, 3, 3, 3, 2, 1, 1, 16, 1
Offset: 0

Views

Author

Klaus Brockhaus, Nov 05 2002

Keywords

Comments

Base-3 analog of A066057 (base 2), A075685 (base 4) and A033665 (base 10). a(103) = -1 is a conjecture (cf. A066450, A077408). For values of n such that presumably a(n) = -1 see A077404.

Examples

			17 (decimal) = 122 -> 122 + 221 = 1120 -> 1120 + 211 = 2101 -> 2101 + 1012 = 10120 -> 10120 + 2101 = 12221 (palindrome) = 160 (decimal) requires 4 steps, so a(17) = 4.
		

Crossrefs

Programs

  • ARIBAS
    m := 120; stop := 1000; for n := 0 to m do v := -1; c := 0; k := n; while c < stop do d := k; rev := 0; while d > 0 do rev := 3*rev + (d mod 3); d := d div 3; end; if k = rev then v := c; c := stop; else inc(c); k := k + rev; end; end; write(v,","); end;

A077403 In base 3: smallest number that requires n Reverse and Add! steps to reach a palindrome.

Original entry on oeis.org

0, 3, 5, 15, 17, 263, 170, 509, 491, 322, 266, 222, 161, 494, 260, 106, 95, 78, 53, 2425, 1466, 9717, 59583, 38878, 38798, 33515, 39440, 32857, 37340, 238849, 177470, 60019, 59655, 178540, 124895, 59753, 179751, 1595576, 715615, 354605, 179575
Offset: 0

Views

Author

Klaus Brockhaus, Nov 05 2002

Keywords

Comments

Base 3 analog of A066058 (base 2), A077441 (base 4) and A023109 (base 10).

Examples

			5 is the smallest number which requires two steps to reach a base 3 palindrome (cf. A066057), so a(2) = 5; 5 (decimal) = 12 -> 12 + 21 = 110 -> 110 + 011 = 121 (palindrome) = 16 (decimal).
		

Crossrefs

Programs

  • ARIBAS
    var ar: array; end; m := 45; ar := alloc(array, m+1, -1); mc := m+1; n := 0; while mc > 0 do v := -1; c := 0; k := n; while c < m+1 do d := k; rev := 0; while d > 0 do rev := 3*rev+(d mod 3); d := d div 3; end; if k = rev then v := c; c := m+1; else inc(c); k := k+rev; end; end; if 0 <= v and v <= m then if ar[v] < 0 then ar[v] := n; dec(mc); write((v,n)); end; end; inc(n); end; writeln(); for j := 0 to m do write(ar[j],","); end;
Previous Showing 11-19 of 19 results.