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 1-2 of 2 results.

A071241 Arithmetic mean of k and R(k) where k is the n-th nonnegative number using only even digits and R(k) is its digit reversal (A004086).

Original entry on oeis.org

0, 2, 4, 6, 8, 11, 22, 33, 44, 55, 22, 33, 44, 55, 66, 33, 44, 55, 66, 77, 44, 55, 66, 77, 88, 101, 202, 303, 404, 505, 121, 222, 323, 424, 525, 141, 242, 343, 444, 545, 161, 262, 363, 464, 565, 181, 282, 383, 484, 585, 202, 303, 404, 505, 606, 222, 323, 424, 525
Offset: 0

Views

Author

Amarnath Murthy, May 20 2002

Keywords

Comments

Conjecture: 101 is the largest prime term, the only other primes being 2 and 11.
The conjecture is false: for example, 181 and 383 are prime terms. There are 150 prime terms less than 75000. - Harvey P. Dale, Sep 02 2016

Crossrefs

Programs

  • Maple
    reversal := proc(n) local i, len, new, temp: new := 0: temp := n: len := floor(log[10](n+.1))+1: for i from 1 to len do new := new+irem(temp, 10)*10^(len-i): temp := floor(temp/10): od: RETURN(new): end: alleven := proc(n) local i, flag, len, temp: temp := n: flag := 1: if n=0 then flag := 0 fi: len := floor(log[10](n+.1))+1: for i from 1 to len do if irem(temp, 10) mod 2 = 0 then temp := floor(temp/10) else flag := 0 fi: od: RETURN(flag): end: for n from 0 to 500 by 2 do if alleven(n) = 1 then printf(`%d,`,(n+reversal(n))/2) fi: od: # James Sellers, May 28 2002
  • Mathematica
    Mean[{#,IntegerReverse[#]}]&/@(FromDigits/@Tuples[{0,2,4,6,8},3]) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 02 2016 *)

Formula

{k + R(k)}/2 where k uses only odd digits 0, 2, 4, 6 and 8.
a(n) = (A014263(n) + A004086(A014263(n))) / 2. - Sean A. Irvine, Jul 06 2024

Extensions

More terms from James Sellers, May 28 2002
Corrected by Harvey P. Dale, Sep 02 2016

A071242 Arithmetic mean of n and R(n) where n is a number such that the least significant digit and the most significant digits are of same parity and R(n) is its digit reversal (A004086).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 11, 22, 33, 44, 55, 22, 33, 44, 55, 66, 22, 33, 44, 55, 66, 33, 44, 55, 66, 77, 33, 44, 55, 66, 77, 44, 55, 66, 77, 88, 44, 55, 66, 77, 88, 55, 66, 77, 88, 99, 101, 202, 303, 404, 505, 111, 212, 313, 414, 515, 121
Offset: 0

Views

Author

Amarnath Murthy, May 20 2002

Keywords

Crossrefs

Programs

  • Maple
    reversal := proc(n) local i, len, new, temp: new := 0: temp := n: len := floor(log[10](n+.1))+1: for i from 1 to len do new := new+irem(temp, 10)*10^(len-i): temp := floor(temp/10): od: RETURN(new): end: for n from 0 to 500 do if type((n+reversal(n))/2, integer) then printf(`%d,`,(n+reversal(n))/2) fi: od: # James Sellers, May 28 2002

Formula

{n + R(n)}/2 for all n which yield integers.

Extensions

More terms from James Sellers, May 28 2002
Showing 1-2 of 2 results.