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 1-10 of 16 results. Next

A077594 Smallest number whose Reverse and Add! trajectory (presumably) contains exactly n palindromes, or -1 if there is no such number.

Original entry on oeis.org

196, 89, 49, 18, 9, 14, 7, 6, 3, 4, 2, 1, 10000, -1, -1, -1, -1, -1, -1, -1, -1
Offset: 0

Views

Author

Klaus Brockhaus, Nov 08 2002

Keywords

Comments

Conjecture 1: For each k > 0 the trajectory of k eventually leads to a term in the trajectory of some j which belongs to A063048, i.e. whose trajectory (presumably) never leads to a palindrome. Conjecture 2: There is no k > 0 such that the trajectory of k contains more than twelve palindromes, i.e. a(n) = -1 for n > 12.

Examples

			a(9) = 4 since the trajectory of 4 contains the nine palindromes 4, 8, 77, 1111, 2222, 4444, 8888, 661166, 3654563 and at 7309126 joins the trajectory of 10577 = A063048(6) and no m < 4 contains exactly nine palindromes.

Links

Crossrefs

Cf. A002113, A006960, A023108, A063048, A063433, A065001, A070742.

A070743 n sets a new record for the index of the (presumably) last palindrome in the 'Reverse and Add' trajectory of n.

Original entry on oeis.org

1, 3, 5, 122, 160, 190, 739, 10000, 10058, 10151, 1003346, 1304392, 1702190
Offset: 1

Views

Author

Klaus Brockhaus, May 03 2002

Keywords

Comments

A070744 gives the corresponding records.

Examples

			678736545637876 is the 36th term and (presumably) the last palindrome in the trajectory of 5; for k < 5 the last palindrome has an index < 36 in the trajectory of k (cf. A070742), so 5 is in the sequence.

Links

Crossrefs

Cf. A065001, A065198, A070742, A070744.

Extensions

Offset corrected by Sean A. Irvine, Jun 11 2024

A070744 Records for the index of the (presumably) last palindrome in the 'Reverse and Add' trajectory of n.

Original entry on oeis.org

18, 32, 36, 37, 38, 39, 40, 54, 80, 82, 100, 101, 102
Offset: 1

Views

Author

Klaus Brockhaus, May 03 2002

Keywords

Comments

Successive maxima in sequence A070742. A070743 gives the corresponding integers at which these records are attained.

Links

Crossrefs

Cf. A065001, A065199, A070742, A070743.

Extensions

Offset corrected by Sean A. Irvine, Jun 11 2024

A090069 Numbers n such that there are (presumably) eight palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

3, 8, 20, 22, 100, 101, 116, 122, 139, 151, 160, 215, 221, 238, 313, 314, 320, 337, 343, 413, 436, 512, 611, 634, 696, 710, 717, 727, 733, 832, 931, 1004, 1011, 1070, 1101, 1160, 1250, 1340, 1430, 1520, 1610, 1700, 1771, 2000, 2002, 2003, 2010, 2100, 2112
Offset: 1

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

For terms <= 5000 each palindrome is reached from the preceding one or from the start in at most 15 steps; after the presumably last one no further palindrome is reached in 2000 steps.

Examples

			The trajectory of 8 begins 8, 16, 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 8, 77, 1111, 2222, 4444, 8888, 661166 and 3654563 are the eight palindromes in the trajectory of 8 and 8 is a term.

Links

Crossrefs

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

A090070 Numbers n such that there are (presumably) nine palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

4, 10, 11, 535, 1000, 1001, 10007, 10101, 20006, 30005, 50003, 60002, 70001, 80000, 80008, 100070, 110060, 120050, 130040, 140030, 150020, 160010, 170000, 170071, 200000, 200002, 1000003, 1000150, 1001001, 1010050, 1100140, 1110040, 1200130
Offset: 1

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

For terms < 5000000 each palindrome is reached from the preceding one or from the start in at most 35 steps; after the presumably last one no further palindrome is reached in 2000 steps.

Examples

			The trajectory of 4 begins 4, 8, 16, 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 4, 8, 77, 1111, 2222, 4444, 8888, 661166 and 3654563 are the nine palindromes in the trajectory of 4 and 4 is a term.

Links

Crossrefs

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

A090071 Numbers n such that there are (presumably) ten palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

2, 5, 10003, 30001, 40000, 40004, 100000, 100001, 2000000, 2000002
Offset: 1

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

Additional terms are 20000000, 20000002, 200000000, 200000002, 2000000000, 2000000002, 10000000004, 10000100001, 20000000000, 20000000002, 20000000003, 30000000002, 40000000001, but it is not yet ascertained that they are consecutive.
For all terms given above each palindrome is reached from the preceding one or from the start in at most 35 steps; after the presumably last one no further palindrome is reached in 5000 steps.

Examples

			The trajectory of 2 begins 2, 4, 8, 16, 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 2, 4, 8, 77, 1111, 2222, 4444, 8888, 661166 and 3654563 are the ten palindromes in the trajectory of 2 and 2 is a term.

Links

Crossrefs

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

A090072 Numbers n such that there are (presumably) eleven palindromes in the Reverse and Add! trajectory of n.

Original entry on oeis.org

1, 20000, 20002, 1000000, 1000001, 10000000, 10000001
Offset: 1

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

Additional terms (cf. A090075) are 100000000, 100000001, 100010001, 1000000000, 1000000001, 10000000000, 10000000001, 100000000000, 100000000001, 1000000000000, 1000000000001, 1000001000001, 1000100010001, but it is not yet ascertained that they are consecutive.
For all terms given above each palindrome is reached from the preceding one or from the start in at most 35 steps; after the presumably last one no further palindrome is reached in 5000 steps.
Only two numbers are known whose Reverse and Add trajectory contains twelve palindromes: 10000 and 10001. It is conjectured that these are the only such numbers and it has been conjectured before (cf. A077594) that no Reverse and Add trajectory contains more than twelve palindromes.

Examples

			The trajectory of 1 begins 1, 2, 4, 8, 16, 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 1, 2, 4, 8, 77, 1111, 2222, 4444, 8888, 661166 and 3654563 are the eleven palindromes in the trajectory of 1 and 1 is a term.

Links

Crossrefs

Cf. A023108, A023109, A065001, A070742, A077594, A090075.

A090075 (Presumed) number of palindromes in the Reverse and Add! trajectory of 10^n.

Original entry on oeis.org

11, 9, 8, 9, 12, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
Offset: 0

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

The absolute maximum 12 at n = 4 and a(n) = 11 for n > 5 support the conjecture (cf. A077594) that there is no positive integer whose trajectory contains more than twelve palindromes.
The last palindrome in the Reverse and Add! trajectory of 10^n is given in A090074.

Links

Crossrefs

Cf. A065001, A070742, A077594, A090069, A090070, A090071, A090072, A090074.

A090074 (Presumed) last palindrome in the Reverse and Add! trajectory of 10^n.

Original entry on oeis.org

3654563, 678736545637876, 663305503366, 663787366, 88352682264077046228625388, 365468864563, 3654566654563, 36545633654563, 365456303654563, 3654563003654563, 36545630003654563, 365456300003654563
Offset: 0

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

No further palindrome is reached in 5000 steps.
The number of palindromes in the Reverse and Add! trajectory of 10^n is given in A090075.

Links

Crossrefs

Cf. A065001, A070742, A077594, A090069, A090070, A090071, A090072, A090075.

Formula

a(n) = 3654563*10^(n) + 3654563 for n > 5.

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

Views

Author

Klaus Brockhaus, Nov 20 2003

Keywords

Comments

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.

Examples

			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.

Links

Crossrefs

Cf. A023108, A023109, A065001, A070742, A077594.
Showing 1-10 of 16 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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