A063048 -id:A063048 - cp's OEIS frontend

A089522 a(n) = smallest non-palindromic number k such that the Reverse and Add! trajectory of k joins the trajectory of A089521(n).

19098, 199998, 990999, 1909098, 19002998, 9905999, 11009094, 19003098, 19005098, 19007098, 19999998, 190009098, 990959999, 990969999, 1990029998, 1990049998, 1990069998, 1990089998, 999079999, 1999049998, 1999069998

Offset: 1

Klaus Brockhaus, Nov 10 2003

Terms of A063048 that are not terms of A088753 (not in ascending order). a(n) > A088753(n). a(n) is the substitute so to speak of A088753(n) in A063048.

a(12), a(15) to a(18), a(20), a(21) are conjectural; it is not yet ensured that they are minimal.

			The trajectories of A088753(1) = 9999 and of 19098 join at 2089791 and there is no number between 9999 and 19098 whose trajectory joins that of 9999.

Index entries for sequences related to Reverse and Add!

Cf. A063048, A088753, A089521.

A243824 Two-column array A(n,s) of pairs (n,s) read by row where s is the smallest seed number such that the Reverse and Add! trajectory of s contains n (excluding cases where n=s).

Original entry on oeis.org

2, 1, 4, 1, 6, 3, 8, 1, 10, 5, 11, 5, 12, 3, 14, 7, 16, 1, 18, 9, 22, 5

Offset: 2

Felix Fröhlich, Jun 11 2014

			A(10,1)=16 is in the array because 16 is the 9th number appearing in the Reverse and Add! trajectory of a smaller number.
A(10,2)=1 is in the array because 1 + 1 = 2, 2 + 2 = 4, 4 + 4 = 8, 8 + 8 = 16, so 1 is the smallest seed number whose Reverse and Add! trajectory contains 16.
Array begins:
  2 1
  4 1
  6 3
  8 1
  10 5
  11 5
  12 3
  14 7
  16 1
  18 9
  22 5

Felix Fröhlich, C++ program for this sequence

Cf. A006960, A023109, A033665, A063048, A070788, A077594.

A070001 Palindromic integers > 0, whose 'Reverse and Add!' trajectory (presumably) does not lead to another palindrome.

Original entry on oeis.org

4994, 8778, 9999, 11811, 19591, 22822, 23532, 23632, 23932, 24542, 24742, 24842, 24942, 26362, 27372, 29792, 29892, 33933, 34543, 34743, 34943, 39493, 44744, 46064, 46164, 46364, 46564, 46964, 47274, 47574, 48284, 48584, 48684, 48884

Offset: 1

Klaus Brockhaus, May 06 2002

The computation of a trajectory was stopped when in 1000 steps no further palindrome appeared. Subsequence of A002113 and of A023108.

			The initial terms of the trajectory of the palindromic integer 8778 are 8778, 17556, 83127 and 83127 is the third term in the trajectory of 7059 (see A063057) which (presumably) never leads to a palindrome (see A063048), so 8778 is in the present sequence.

Index entries for sequences related to Reverse and Add!

Cf. A002113, A023108, A063057, A063048.

{stop=1000; for(k=1,50000,m=k; c=0; p=1; while(c0,d=divrem(n,10); n=d[1]; rev=10*rev+d[2]); if(m==k&&rev!=m,p=0); if(m>k&&rev==m,p=0); m=m+rev; c++); if(c==stop&&p==1,print1(k,",")))}

A090062 There is (presumably) one and only one palindrome in the Reverse and Add! trajectory of n.

Original entry on oeis.org

89, 98, 167, 187, 266, 286, 365, 385, 479, 563, 578, 583, 662, 677, 682, 749, 761, 776, 779, 781, 829, 860, 869, 875, 880, 899, 928, 947, 968, 974, 977, 998, 1077, 1093, 1098, 1167, 1183, 1188, 1257, 1273, 1278, 1297, 1347, 1363, 1368, 1387, 1396, 1397, 1437

Offset: 1

Klaus Brockhaus, Nov 20 2003

For terms < 2000 the only palindrome is reached from the start in at most 24 steps; thereafter no further palindrome is reached in 2000 steps.

			The trajectory of 479 begins 479, 1453, 4994, 9988, 18887, ...; at 9988 it joins the (presumably) palindrome-free trajectory of A063048(3) = 1997, hence 4994 is the only palindrome in the trajectory of 479 and 479 is a term.

Index entries for sequences related to Reverse and Add!

Cf. A023108, A023109, A065001, A070742, A077594.

A090063 Numbers n such that there are (presumably) two palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

49, 58, 67, 76, 85, 94, 108, 118, 127, 133, 143, 148, 153, 173, 177, 178, 198, 207, 217, 226, 239, 247, 276, 277, 279, 297, 306, 316, 325, 331, 338, 339, 341, 346, 349, 351, 371, 375, 376, 378, 379, 396, 405, 415, 419, 430, 437, 438, 440, 445, 448, 450, 464

Offset: 1

Klaus Brockhaus, Nov 20 2003

For terms < 2000 each palindrome is reached from the preceding one or from the start in at most 24 steps; after the presumably last one no further palindrome is reached in 2000 steps.

			The trajectory of 118 begins 118, 929, 1858, 10439, 103840, 152141, 293392, 586784, 1074469, ...; at 1074469 it joins the (presumably) palindrome-free trajectory of A063048(72) = 90379, hence 929 and 293392 are the two palindromes in the trajectory of 118 and 118 is a term.

Index entries for sequences related to Reverse and Add!

Cf. A023108, A023109, A065001, A070742, A077594.

A090064 Numbers n such that there are (presumably) three palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

18, 27, 36, 45, 54, 63, 69, 72, 78, 81, 87, 90, 96, 99, 113, 125, 126, 128, 137, 146, 149, 156, 157, 162, 163, 165, 168, 169, 172, 175, 180, 183, 188, 189, 193, 194, 195, 197, 220, 224, 225, 227, 232, 236, 242, 245, 248, 252, 255, 256, 259, 261, 264, 267, 268

Offset: 1

Klaus Brockhaus, Nov 20 2003

For terms < 2000 each palindrome is reached from the preceding one or from the start in at most 24 steps; after the presumably last one no further palindrome is reached in 2000 steps.

			The trajectory of 113 begins 113, 424, 848, 1696, 8657, 16225, 68486, 136972, 416603, ...; at 416603 it joins the (presumably) palindrome-free trajectory of A063048(16) = 10735, hence 424, 848 and 68486 are the three palindromes in the trajectory of 113 and 113 is a term.

Index entries for sequences related to Reverse and Add!

Cf. A023108, A023109, A065001, A070742, A077594.

A090065 Numbers n such that there are (presumably) four palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

9, 19, 28, 29, 37, 38, 39, 46, 47, 48, 56, 57, 64, 65, 73, 74, 75, 82, 83, 84, 91, 92, 93, 110, 112, 121, 124, 132, 134, 135, 136, 138, 144, 147, 155, 164, 166, 174, 182, 186, 190, 192, 211, 212, 219, 223, 229, 230, 231, 233, 234, 235, 237, 240, 243, 246, 249

Offset: 1

Klaus Brockhaus, Nov 20 2003

For terms < 2000 each palindrome is reached from the preceding one or from the start in at most 24 steps; after the presumably last one no further palindrome is reached in 2000 steps.

			The trajectory of 134 begins 134, 565, 1130, 1441, 2882, 5764, 10439, 103840, 152141, 293392, 586784, 1074469, ...; at 1074469 it joins the (presumably) palindrome-free trajectory of A063048(72) = 90379, hence 565, 1441, 2882 and 293392 are the four palindromes in the trajectory of 134 and 134 is a term.

Index entries for sequences related to Reverse and Add!

Cf. A023108, A023109, A065001, A070742, A077594.

A090066 Numbers n such that there are (presumably) five palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

14, 15, 23, 24, 32, 41, 42, 50, 51, 55, 60, 66, 79, 97, 105, 106, 107, 119, 120, 123, 129, 130, 131, 140, 141, 152, 159, 161, 171, 176, 179, 181, 184, 185, 199, 204, 205, 206, 218, 228, 251, 258, 269, 275, 278, 283, 284, 290, 298, 304, 305, 317, 319, 321, 327

Offset: 1

Klaus Brockhaus, Nov 20 2003

For terms < 2000 each palindrome is reached from the preceding one or from the start in at most 24 steps; after the presumably last one no further palindrome is reached in 2000 steps.

			The trajectory of 106 begins 106, 707, 1414, 5555, 11110, 12221, 24442, 48884, 97768, ...; at 97768 it joins the (presumably) palindrome-free trajectory of A063048(3) = 1997, hence 707, 5555, 12221, 24442 and 48884 are the five palindromes in the trajectory of 106 and 106 is a term.

Index entries for sequences related to Reverse and Add!

Cf. A023108, A023109, A065001, A070742, A077594.

A090067 Numbers n such that there are (presumably) six palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

7, 12, 17, 21, 26, 30, 33, 35, 53, 59, 62, 68, 71, 80, 86, 88, 95, 102, 103, 109, 114, 117, 142, 150, 154, 170, 191, 201, 208, 209, 210, 213, 216, 222, 241, 253, 300, 301, 303, 307, 308, 312, 315, 329, 340, 352, 359, 383, 389, 400, 404, 406, 407, 411, 428, 451

Offset: 1

Klaus Brockhaus, Nov 20 2003

For terms < 2000 each palindrome is reached from the preceding one or from the start in at most 24 steps; after the presumably last one no further palindrome is reached in 2000 steps.

			The trajectory of 154 begins 154, 605, 1111, 2222, 4444, 8888, 17776, 85547, 160105, 661166, 1322332, 3654563, 7309126, ...; at 7309126 it joins the (presumably) palindrome-free trajectory of A063048(7) = 10577, hence 525, 1551, 5115, 13431, 26862 and 12455421 are the six palindromes in the trajectory of 154 and 154 is a term.

Index entries for sequences related to Reverse and Add!

Cf. A023108, A023109, A065001, A070742, A077594.

A090068 Numbers n such that there are (presumably) seven palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

6, 13, 16, 25, 31, 34, 40, 43, 44, 52, 61, 70, 77, 104, 111, 115, 145, 158, 200, 202, 203, 214, 244, 250, 257, 302, 356, 399, 401, 412, 414, 442, 455, 498, 500, 505, 511, 519, 529, 541, 554, 597, 610, 618, 626, 628, 640, 653, 656, 686, 752, 795, 797, 816, 826

Offset: 1

Klaus Brockhaus, Nov 20 2003

For terms < 2000 each palindrome is reached from the preceding one or from the start in at most 24 steps; after the presumably last one no further palindrome is reached in 2000 steps.

			The trajectory of 25 begins 25, 77, 154, 605, 1111, 2222, 4444, 8888, 17776, 85547, 160105, 661166, 1322332, 3654563,7309126, ...; at 7309126 it joins the (presumably) palindrome-free trajectory of A063048(7) = 10577, hence 77, 1111, 2222, 4444, 8888, 661166 and 3654563 are the seven palindromes in the trajectory of 25 and 25 is a term.

Index entries for sequences related to Reverse and Add!

Cf. A023108, A023109, A065001, A070742, A077594.

cp's OEIS Frontend

A089522 a(n) = smallest non-palindromic number k such that the Reverse and Add! trajectory of k joins the trajectory of A089521(n).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A243824 Two-column array A(n,s) of pairs (n,s) read by row where s is the smallest seed number such that the Reverse and Add! trajectory of s contains n (excluding cases where n=s).

Views

Author

Keywords

Examples

Links

Crossrefs

A070001 Palindromic integers > 0, whose 'Reverse and Add!' trajectory (presumably) does not lead to another palindrome.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A090062 There is (presumably) one and only one palindrome in the Reverse and Add! trajectory of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A090063 Numbers n such that there are (presumably) two palindromes in the Reverse and Add! trajectory of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A090064 Numbers n such that there are (presumably) three palindromes in the Reverse and Add! trajectory of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A090065 Numbers n such that there are (presumably) four palindromes in the Reverse and Add! trajectory of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A090066 Numbers n such that there are (presumably) five palindromes in the Reverse and Add! trajectory of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A090067 Numbers n such that there are (presumably) six palindromes in the Reverse and Add! trajectory of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A090068 Numbers n such that there are (presumably) seven palindromes in the Reverse and Add! trajectory of n.

Views

Author

Keywords

Comments

Examples