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.

A334528 Palindromic numbers that are also Niven numbers and Smith numbers.

This page as a plain text file.
%I A334528 #8 May 06 2020 01:46:43
%S A334528 4,666,28182,45054,51315,82628,239932,454454,864468,2594952,2976792,
%T A334528 3189813,3355533,4172714,4890984,5319135,5367635,5777775,7149417,
%U A334528 7247427,8068608,8079708,8100018,8280828,8627268,9227229,9423249,21699612,22544522,24166142,27677672
%N A334528 Palindromic numbers that are also Niven numbers and Smith numbers.
%C A334528 Witno (2014) proved that this sequence is infinite.
%H A334528 Amiram Eldar, <a href="/A334528/b334528.txt">Table of n, a(n) for n = 1..512</a>
%H A334528 Amin Witno, <a href="https://www.emis.de/journals/INTEGERS/papers/o66/o66.Abstract.html">Smith Numbers With Extra Digital Features</a>, Integers, Vol. 14 (2014), Article A66.
%e A334528 666 is a term since it is palindromic, a Niven number (6 + 6 + 6 = 18 is a divisor of 666) and a Smith number (666 = 2 * 3 * 3 * 37 and 6 + 6 + 6 = 2 + 3 + 3 + 3 + 7).
%t A334528 digSum[n_] := Plus @@ IntegerDigits[n]; palNivenSmithQ[n_] := PalindromeQ[n] && Divisible[n, (ds = digSum[n])] && CompositeQ[n] && Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) == ds; Select[Range[10^5], palNivenSmithQ]
%Y A334528 Intersection of A002113, A005349 and A006753.
%Y A334528 Intersection of any two of the sequences A082232, A098834 and A334527.
%K A334528 nonn,base
%O A334528 1,1
%A A334528 _Amiram Eldar_, May 05 2020