A067031 -id:A067031 - cp's OEIS frontend

A067287 n sets a new record for the number of integers k such that k is not of the form m + reverse(m) for any m and n occurs in the 'Reverse and Add' trajectory of k (cf. A067284).

0, 22, 33, 44, 66, 88, 110, 121, 242, 484, 968, 1837, 2222, 3102, 4444, 4884, 7106, 8888, 12221, 24442, 44044, 48884, 88088, 176176, 293392, 295482, 466664, 597795, 688886, 711106, 797797, 930028, 933328, 997799, 1112111, 1197801, 1686861

Offset: 0

Klaus Brockhaus, Feb 04 2002

A067288 gives the corresponding records.

			33 belongs to the sequence because three integers k (viz. 3, 21, 30) are not of the form j + reverse(j) for any j and 33 occurs in the "Reverse and Add!" trajectory of these k and for m < 33 there are at most two integers which have the corresponding property.

Index entries for sequences related to Reverse and Add!

Cf. A067030, A067031, A067032, A067035, A067036, A067284, A067288.

More terms from Larry Reeves (larryr(AT)acm.org), Dec 18 2002

A067288 Records for the number of integers k such that k is not of the form m + reverse(m) for any m and for some n A067030(n) occurs in the 'Reverse and Add' trajectory of k (cf. A067284).

Original entry on oeis.org

1, 2, 3, 5, 8, 12, 13, 21, 22, 30, 38, 39, 42, 46, 71, 90, 94, 150, 254, 286, 404, 434, 578, 586, 602, 643, 758, 799, 813, 847, 1131, 1162, 1169, 1334, 1742, 2093, 2120, 2378, 2663, 2892, 3208, 3383, 3585, 3685, 3999, 4818, 4942, 5766, 5959

Offset: 1

Klaus Brockhaus, Feb 04 2002

Successive maxima in sequence A067284. A067287 gives the corresponding integers at which these records are attained.

			3 is a record, since for A067030(12) = 33 there are three integers k not of the form j + reverse(j) for any j such that 33 occurs in the "Reverse and Add!" trajectory of these k and for m < 33 there are at most two integers which have the corresponding property.

Index entries for sequences related to Reverse and Add!

Cf. A067030, A067031, A067032, A067035, A067036, A067284, A067287.

More terms from Larry Reeves (larryr(AT)acm.org), Dec 18 2002

Offset and a(27) onward corrected by Sean A. Irvine, Dec 12 2023

A068061 Palindromic numbers j that are not of the form k + reverse(k) for any k.

Original entry on oeis.org

1, 3, 5, 7, 9, 111, 131, 151, 171, 191, 212, 232, 252, 272, 292, 313, 333, 353, 373, 393, 414, 434, 454, 474, 494, 515, 535, 555, 575, 595, 616, 636, 656, 676, 696, 717, 737, 757, 777, 797, 818, 838, 858, 878, 898, 919, 939, 959, 979, 999, 10101, 10301, 10501

Offset: 1

Klaus Brockhaus, Feb 15 2002

Intersection of A002113 and A067031. Every palindrome with an even number of digits is of the form k + reverse(k), for example 123321 = 123000 + 000321, so the sequence has no terms with an even number of digits.
It seems that the terms follow a strict pattern: x1x', x3x', x5x', x7x', x9x', y1y', y3y', y5y', y7y', y9y' and so on. x' is reverse(x). Apart from the first 5 terms in the sequence, the surrounding terms (x and y) simply iterate over the positive integers. - Dmitry Kamenetsky, Mar 10 2017
Every palindrome with an odd number of digits is of the form k + reverse(k) if the central digit is even, for example 1234321 = 1232000 + 0002321, so no term with an odd number of digits has an even central digit. - A.H.M. Smeets, Feb 01 2019

			9 belongs to this sequence, since there is no k such that k + reverse(k) = 9 (cf. A067031).

Michel Marcus, Table of n, a(n) for n = 1..500

Cf. A002113, A067031, A068062.

isok(n) = {if (Pol(d=digits(n)) == Polrev(d), for (k=1, n-1, if (k + fromdigits(Vecrev(digits(k))) == n, return (0));); 1;);} \\ Michel Marcus, Mar 12 2017

A091679 In base 4, numbers n not of the form k + reverse(k) for any k.

Original entry on oeis.org

1, 3, 7, 8, 9, 11, 12, 13, 14, 16, 18, 19, 21, 22, 23, 24, 26, 27, 28, 29, 31, 32, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 49, 52, 53, 54, 55, 56, 57, 60, 61, 62, 63, 64, 66, 69, 70, 71, 72, 73, 74, 77, 78, 79, 80, 81, 82, 83, 86, 87, 88, 89, 90, 91, 94, 95, 96, 97, 98

Offset: 0

Klaus Brockhaus, Jan 28 2004

Base-4 analog of A067031. Complement of A091678.

			31 is a term since 31 (decimal) = 133 and there is no k such that k + reverse(k) = 133 in base 4.

Cf. A091678, A067031.

A067737 Integers n such that [number of integers k such that k is not of the form m + reverse(m) for any m and n occurs in the "Reverse and Add!" trajectory of k] is greater than [number of integers k such that n = k + reverse(k)].

Original entry on oeis.org

44, 66, 88, 110, 121, 132, 154, 176, 198, 242, 363, 404, 444, 484, 505, 524, 545, 564, 585, 605, 606, 625, 646, 665, 686, 707, 726, 747, 766, 787, 808, 827, 847, 848, 867, 888, 909, 928, 949, 968, 989, 1010, 1029, 1050, 1069, 1089, 1090, 1111, 1130, 1151

Offset: 1

Klaus Brockhaus, Feb 04 2002

Integers n such that n = A067030(j) for some j and A067284(j) > A067032(j).

			44 = A067030(13) is in the sequence, since there are five integers k (viz. 5, 13, 20, 31, 40; A067284(13) = 5) such that k is not of the form m + reverse(m) for any m and 44 occurs in the "Reverse and Add!" trajectory of k, but only four integers k (viz. 13, 22, 31, 40; A067032(13) = 4) such that 44 = k + reverse(k).

Index entries for sequences related to Reverse and Add!

Cf. A067030, A067031, A067032, A067284.

A092214 In base 2: numbers n not of the form k + reverse(k) for any k.

Original entry on oeis.org

1, 4, 7, 8, 11, 12, 13, 16, 19, 20, 22, 23, 26, 28, 29, 31, 32, 36, 38, 39, 40, 41, 43, 46, 47, 48, 49, 50, 53, 55, 56, 58, 59, 60, 61, 64, 67, 68, 70, 71, 72, 73, 74, 76, 77, 79, 80, 82, 83, 86, 87, 88, 89, 91, 92, 94, 95, 97, 98, 100, 103, 104, 106, 107, 109, 110, 111, 112

Offset: 0

Klaus Brockhaus, Feb 25 2004

Base-2 analog of A067031 (base 10) and A091679 (base 4). Complement of A092213.

			13 is a term since 13 (decimal) = 1101 and there is no k such that k + reverse(k) = 1101 in base 2.

Cf. A092213, A067031, A091679.

A298972 Number of positive integers k < n such that n occurs in the Reverse-and-Add trajectory of k.

Original entry on oeis.org

0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 2, 2, 0, 1, 0, 4, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Felix Fröhlich, Jan 30 2018

Number of integers k < n such that n occurs in row k of A243238.
For n > 0, a(n) = 0 iff n is a term of A067031.
For n > 0, a(n) > 0 iff n is a term of A067030.

			For n = 22: There exist 4 positive integers k < 22 such that 22 occurs in the Reverse-and-Add trajectory of k, namely 5, 10, 11 and 20, so a(22) = 4.

Index entries for sequences related to Reverse and Add!

Cf. A056964, A067030, A067031, A243238.

Block[{nn = 85, s}, s = Array[Union@ NestWhileList[# + IntegerReverse@ # &, #, # < nn &, 1, nn] &, nn]; Array[Count[Take[s, # - 1], #, 2] &, nn + 1, 0]] (* Michael De Vlieger, Feb 01 2018 *)

a(n) = my(i=0); for(k=1, n-1, my(x=k); while(x < n, x=x+eval(concat(Vecrev(Str(x))))); if(x==n, i++)); i

A068798 Integers n such that n = A067030(j) for some j and A067286(j) < A067034(j).

Original entry on oeis.org

4, 8, 11, 12, 16, 121, 198, 1717, 1757, 1797, 1818, 1837, 1858, 1877, 1898, 1938, 1978, 11011, 17127, 18018, 18887, 19998, 111001, 113201, 115401, 117601, 119801, 170217, 170617, 171017, 171227, 171417, 171627, 171817, 172027, 172427, 172827, 180018, 180418

Offset: 1

Klaus Brockhaus, Mar 05 2002

Integers n such that n = A067030(j) for some j and [largest integer k such that k is not of the form m + reverse(m) for any m (cf. A067031) and n occurs in the 'Reverse and Add' trajectory of k.] is smaller than [largest k such that n = k + reverse(k)]. - A067030(j) is a term iff A067034(j) is in A067030.

			4 = A067030(2) is in the sequence, since A067286(2) = 1 < 2 = A067034(2). 121 = A067030(21) is in the sequence, since A067286(21) = 92 < 110 = A067034(21).

Index entries for sequences related to Reverse and Add!

Cf. A067030, A067031, A067034, A067286.

More terms from Sean A. Irvine, Mar 15 2024

cp's OEIS Frontend

A067287 n sets a new record for the number of integers k such that k is not of the form m + reverse(m) for any m and n occurs in the 'Reverse and Add' trajectory of k (cf. A067284).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A067288 Records for the number of integers k such that k is not of the form m + reverse(m) for any m and for some n A067030(n) occurs in the 'Reverse and Add' trajectory of k (cf. A067284).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A068061 Palindromic numbers j that are not of the form k + reverse(k) for any k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A091679 In base 4, numbers n not of the form k + reverse(k) for any k.

Views

Author

Keywords

Comments

Examples

Crossrefs

A067737 Integers n such that [number of integers k such that k is not of the form m + reverse(m) for any m and n occurs in the "Reverse and Add!" trajectory of k] is greater than [number of integers k such that n = k + reverse(k)].

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A092214 In base 2: numbers n not of the form k + reverse(k) for any k.

Views

Author

Keywords

Comments

Examples

Crossrefs

A298972 Number of positive integers k < n such that n occurs in the Reverse-and-Add trajectory of k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

A068798 Integers n such that n = A067030(j) for some j and A067286(j) < A067034(j).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions