A071241 - OEIS

%I #26 Jul 07 2024 07:35:45

%S 0,2,4,6,8,11,22,33,44,55,22,33,44,55,66,33,44,55,66,77,44,55,66,77,

%T 88,101,202,303,404,505,121,222,323,424,525,141,242,343,444,545,161,

%U 262,363,464,565,181,282,383,484,585,202,303,404,505,606,222,323,424,525

%N 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).

%C Conjecture: 101 is the largest prime term, the only other primes being 2 and 11.

%C 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

%H Harvey P. Dale, <a href="/A071241/b071241.txt">Table of n, a(n) for n = 0..10000</a>

%F {k + R(k)}/2 where k uses only odd digits 0, 2, 4, 6 and 8.

%F a(n) = (A014263(n) + A004086(A014263(n))) / 2. - _Sean A. Irvine_, Jul 06 2024

%p 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

%t Mean[{#,IntegerReverse[#]}]&/@(FromDigits/@Tuples[{0,2,4,6,8},3]) (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 02 2016 *)

%Y Cf. A004086, A014263, A071240, A071242.

%K base,nonn

%O 0,2

%A _Amarnath Murthy_, May 20 2002

%E More terms from _James A. Sellers_, May 28 2002

%E Corrected by _Harvey P. Dale_, Sep 02 2016