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).

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

0,2

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

Links

Harvey P. Dale, Table of n, a(n) for n = 0..10000

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

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 A. 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 *)

Crossrefs

Cf. A004086, A014263, A071240, A071242.

Sequence in context: A373644 A164144 A353007 * A247123 A332240 A068062

Adjacent sequences: A071238 A071239 A071240 * A071242 A071243 A071244

Keyword

base,nonn

Author

Amarnath Murthy, May 20 2002

Extensions

More terms from James A. Sellers, May 28 2002

Corrected by Harvey P. Dale, Sep 02 2016

Status

approved