A071242 -id:A071242 - cp's OEIS frontend

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

Amarnath Murthy, May 20 2002

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

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

Cf. A004086, A014263, A071240, A071242.

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

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

{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

More terms from James Sellers, May 28 2002

Corrected by Harvey P. Dale, Sep 02 2016

A071240 Arithmetic mean of k and R(k) where k is a number using only odd digits and R(k) is its digit reversal (A004086).

Original entry on oeis.org

1, 3, 5, 7, 9, 11, 22, 33, 44, 55, 22, 33, 44, 55, 66, 33, 44, 55, 66, 77, 44, 55, 66, 77, 88, 55, 66, 77, 88, 99, 111, 212, 313, 414, 515, 131, 232, 333, 434, 535, 151, 252, 353, 454, 555, 171, 272, 373, 474, 575, 191, 292, 393, 494, 595, 212, 313, 414, 515, 616

Offset: 0

Amarnath Murthy, May 20 2002

Cf. A004086, A014261, A071241, A071242.

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:
allodd := 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 = 1 then temp := floor(temp/10) else flag := 0 fi:
    od:
    RETURN(flag):
end:
for n from 1 to 501 by 2 do
    if allodd(n) = 1 then printf(`%d, `, (n+reversal(n))/2) fi:
od: # James Sellers, May 28 2002

{k + R(k)}/2 where k uses only odd digits 1, 3, 5, 7 and 9.

a(n) = (A014261(n) + A004086(A014261(n))) / 2. - Sean A. Irvine, Jul 06 2024

More terms from James Sellers, May 28 2002

cp's OEIS Frontend

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).

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