A262526 -id:A262526

Search: a262526 -id:a262526

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A262527

Conjectured minimum number of ways to represent a number >= A262526(i) by sums of three base-10 palindromes.

+20
5

1, 2, 3, 4, 5, 6, 8, 11, 13, 14, 15, 16, 17, 18, 21, 27, 29, 35, 41, 45, 48, 51, 54, 55, 56, 61, 63, 64, 65, 74, 75, 79, 80, 82, 83, 85, 86, 87, 91, 111, 112, 113, 114, 115, 116, 118, 120, 121, 124, 127, 133, 134, 138, 140, 141, 142, 145, 147, 150, 153, 165, 169, 171, 174, 175, 177, 179, 180, 183, 184, 185

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The sequence is obtained by sorting the counts A261132 into increasing order together with their positions of occurrence. If a new record in the sorted A261132 is found, the index of its latest occurrence in A261132 becomes the next term in A262526 and the corresponding value of A261132 becomes a(n).

7 is not in the sequence, because the latest occurrence of 7 is at A261132(64), whereas the latest occurrence of 6 had already set the record to A262526(6) = 120.

a(7) = 8 corresponds to the latest occurrence of 8 at A261132(142), thus A262526(7) = 142.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..1072

Hugo Pfoertner, Least number of representations by sums of three palindromes.

EXAMPLE

a(5) = 5 because A261132(k) > 5 for all k > A262526(5) = 98.

CROSSREFS

Cf. A002113, A261132, A262524, A262525, A262526.

See A261422, A262544, A262545 for another approach.

KEYWORD

nonn,base

AUTHOR

Hugo Pfoertner, Sep 25 2015

STATUS

approved

A262544

Records in A261422.

+10
7

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 63, 72, 79, 84, 87, 88, 117, 126, 135, 142, 147, 150, 151, 153, 156, 159, 162, 168, 177, 198, 207, 213, 216, 219, 222, 226, 231, 261, 264, 270, 279, 297, 318, 342, 369, 375, 426, 429, 465, 513, 567, 591, 660, 663, 678, 681, 729, 820, 870, 963, 982, 1005

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

N. J. A. Sloane and Hugo Pfoertner, Table of n, a(n) for n = 1..869 (first 257 terms from N. J. A. Sloane)

Hugo Pfoertner, Logarithmic plot of A262544 vs A262545.

CROSSREFS

Cf. A261132, A261422, A262545, A262524, A262525, A262526, A262527.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 06 2015

STATUS

approved

A262524

Numbers that can be represented as the sum of three base-10 palindromes in more ways than any smaller number. Position of records in A261132.

+10
5

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 110, 143, 165, 187, 303, 323, 345, 373, 383, 393, 413, 446, 454, 464, 474, 484, 494, 504, 514, 544, 565, 575, 585, 595, 605, 615, 635, 686, 696, 706, 716, 726, 736, 746, 797, 807, 817, 827, 837, 898, 908, 918, 928, 938, 948, 999, 1009

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The corresponding representation counts A261132(a(n)) are provided in A262525.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..851

CROSSREFS

Cf. A002113, A261132, A262525, A262526, A262527.

See A261422, A262544, A262545 for another approach.

KEYWORD

nonn,base

AUTHOR

Hugo Pfoertner, Sep 24 2015

STATUS

approved

A262525

Records in the number of ways to represent a number as the sum of three base-10 palindromes, A261132.

+10
5

1, 2, 3, 4, 5, 7, 8, 10, 12, 13, 15, 16, 17, 18, 22, 25, 28, 29, 30, 36, 37, 38, 40, 42, 47, 48, 49, 53, 56, 61, 65, 66, 74, 75, 76, 83, 92, 101, 104, 116, 119, 128, 143, 151, 166, 170, 173, 174, 197, 210, 231, 237, 243, 257, 278, 304, 315, 322, 323, 330, 363, 389, 402, 411, 434, 474, 490, 501, 524, 575

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The positions of the records are provided in A262524.

LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..851

Hugo Pfoertner, Logarithmic plot of A262525 vs A262524.

CROSSREFS

Cf. A002113, A261132, A262524, A262526, A262527.

See A261422, A262544, A262545 for another approach.

KEYWORD

nonn,base

AUTHOR

Hugo Pfoertner, Sep 24 2015

STATUS

approved

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