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 1-6 of 6 results.

A247123 Palindromes obtained after one iteration of Reverse and Add applied to the terms of A015976.

Original entry on oeis.org

2, 4, 6, 8, 11, 22, 33, 44, 55, 66, 77, 88, 99, 22, 33, 44, 55, 66, 77, 88, 99, 121, 33, 44, 55, 66, 77, 88, 99, 121, 44, 55, 66, 77, 88, 99, 121, 55, 66, 77, 88, 99, 121, 66, 77, 88, 99, 121, 77
Offset: 2

Views

Author

Morgan L. Owens, Nov 21 2014

Keywords

Crossrefs

Cf. A015976 (One iteration of Reverse and Add is needed to reach a palindrome).

Programs

  • Mathematica
    Select[(FromDigits[#] + FromDigits[Reverse[#]]) & /@ IntegerDigits[Range[1000]], IntegerDigits[#] == Reverse[IntegerDigits[#]] &]

A065206 Numbers which need one 'Reverse and Add' step to reach a palindrome.

Original entry on oeis.org

10, 12, 13, 14, 15, 16, 17, 18, 20, 21, 23, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 38, 40, 41, 42, 43, 45, 47, 50, 51, 52, 53, 54, 56, 60, 61, 62, 63, 65, 70, 71, 72, 74, 80, 81, 83, 90, 92, 100, 102, 103, 104, 105, 106, 107, 108, 110, 112, 113, 114, 115, 116, 117
Offset: 1

Views

Author

Klaus Brockhaus, Oct 21 2001

Keywords

Comments

The number of steps starts at 0, so palindromes (A002113) are excluded.
Numbers k such that A033665(k) = 1. - Andrew Howroyd, Dec 05 2024

Links

Crossrefs

Cf. A002113, A015976, A033665, A136522, A056964, A029742.
Sequences for 2..12 steps needed are: A065207, A065208, A065209, A065210, A065211, A065212, A065213, A065214, A065215, A065216, A065217.

Programs

  • ARIBAS
    function revadd_steps(k,stop: integer); var c,n,m,steps,rev: integer; begin n := 0; c := 0; while c < stop do m := n; rev := int_reverse(m); steps := 0; while steps < k and m <> rev do m := m + rev; rev := int_reverse(m); inc(steps); end; if steps = k and m = rev then write(n," "); inc(c); end; inc(n); end; end; revadd_steps(1,66).
  • Haskell
    a065206 n = a065206_list !! (n-1)
a065206_list = filter ((== 1) . a136522 . a056964) a029742_list
-- Reinhard Zumkeller, Oct 14 2011
  • Mathematica
    Select[Range[10,120],!PalindromeQ[#]&&PalindromeQ[#+IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 14 2017 *)
  • PARI
    isok(n,s=1)={for(k=0, s, my(r=fromdigits(Vecrev(digits(n)))); if(r==n, return(k==s)); n += r); 0} \\ Andrew Howroyd, Dec 05 2024

Extensions

Offset corrected by Harry J. Smith, Oct 13 2009

A244392 Primes p such that p + (p reversed) is a palindrome.

Original entry on oeis.org

2, 3, 11, 13, 17, 23, 29, 31, 41, 43, 47, 53, 61, 71, 83, 101, 103, 107, 113, 127, 131, 137, 211, 223, 227, 233, 241, 311, 313, 331, 401, 421, 431, 433, 443, 503, 521, 523, 541, 601, 613, 631, 641, 643, 701, 811, 821, 1013, 1021, 1031, 1033, 1051, 1061, 1063
Offset: 1

Views

Author

Vincenzo Librandi, Jul 02 2014

Keywords

Comments

Palindrome is also a prime for n = 241, 443, 613, 641, 811, 20011, 20047, 20051, 20101, 20161, ... . Example: 613+316 = 929, which is prime. [Bruno Berselli, Jul 05 2014]
Subsequence of primes within A015976. - Michel Marcus, Jul 05 2014

Examples

			13 is in the sequence because 13+31 = 44 is a palindrome.
1103 is in the sequence because 1103+3011 = 4114 is a palindrome.

Links

Crossrefs

Cf. A007500, A015976, A061783.

Programs

  • Magma
    [p: p in PrimesUpTo(1200) | q eq Reverse(q) where q is Intseq(p+Seqint(Reverse(Intseq(p))))]; // Bruno Berselli, Jul 05 2014
  • Mathematica
    selQ[p_] := (id = IntegerDigits[p]; id2 = IntegerDigits[p + FromDigits[Reverse[id]]]; id2 == Reverse[id2]); Select[Array[Prime, 200], selQ] (* Jean-François Alcover, Jul 05 2014 *)
Select[Prime[Range[200]],PalindromeQ[#+IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 11 2020 *)

A331214 a(n) and at least one distinct anagram of a(n) that doesn't start with a leading 0 sum up to a palindrome.

Original entry on oeis.org

12, 13, 14, 15, 16, 17, 18, 21, 23, 24, 25, 26, 27, 29, 31, 32, 34, 35, 36, 38, 41, 42, 43, 45, 47, 51, 52, 53, 54, 56, 61, 62, 63, 65, 71, 72, 74, 81, 83, 92, 102, 103, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 118, 120, 122, 123, 124, 125, 126, 127, 128, 132, 133, 134, 135, 136, 137, 138, 142
Offset: 1

Views

Author

Eric Angelini, Jan 12 2020

Keywords

Examples

			10 is not in the sequence although 10 + 01 = 11 because 01 starts with a leading 0;
11 is not in the sequence although 11 + 11 = 22 because the second 11 is not distinct from the first one;
12 is in the sequence as 12 + 21 = 33. Etc.

Links

Crossrefs

Cf. A002113, A015976 ("Reverse and add").

Programs

  • PARI
    See Links section.

A370842 Numbers k that can be added without carries to their digit reversal (A004086(k)).

Original entry on oeis.org

0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33, 34, 35, 36, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 60, 61, 62, 63, 70, 71, 72, 80, 81, 90, 100, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113
Offset: 1

Views

Author

Rémy Sigrist, Mar 03 2024

Keywords

Comments

All positive terms belong to A015976.

Examples

			42 belongs to the sequence as 42 + 24 does not lead to carries.
48 does not belong to the sequence as 48 + 84 leads to carries.

Crossrefs

Cf. A004086, A015976, A056964, A140900 (base-2 analog).

Programs

  • PARI
    is(n, base = 10) = { my (d = if (n, digits(n, base), [0]), p = d + Vecrev(d)); vecmax(p) < base }

A382082 F(k) such that F(k) + (F(k) reversed) is a palindrome, where F(k) is a Fibonacci number.

Original entry on oeis.org

0, 1, 2, 3, 13, 21, 34, 144, 233, 610, 4181, 832040, 102334155, 1134903170, 20365011074, 12200160415121876738
Offset: 1

Views

Author

Vincenzo Librandi, Mar 21 2025

Keywords

Comments

Conjecture: The sequence appears to be finite.
The next term, F(k), has k > 3*10^5, if it exists. - Amiram Eldar, Mar 21 2025

Examples

			144 is in the sequence because 144 + 441 = 585 is a palindrome.

Crossrefs

Intersection of A000045 and A015976.
Cf. A002113, A004086, A004091, A352124.

Programs

  • Magma
    Rev := func;
[0] cat  [Fibonacci(n): n in [2..2*10^4] | q eq Rev(q) where q is Fibonacci(n)+Rev(Fibonacci(n))];
  • Mathematica
    DeleteDuplicates@ Select[Fibonacci[Range[0, 100]], PalindromeQ[# + IntegerReverse[#]] &] (* Amiram Eldar, Mar 21 2025 *)
Showing 1-6 of 6 results.

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