A062916 - OEIS

%I #18 Sep 05 2024 19:15:04

%S 1710,2166,2318,2489,3230,3705,3876,4940,5073,5396,5548,6460,6612,

%T 6783,6935,7068,8132,8455,8607,9690,9842,11134,11457,11609,12692,

%U 12844,13129,14364,14516,14687,14839,15903,16036,16359,17100,17423

%N Non-palindromic number and its reversal are both multiples of 19.

%H Harry J. Smith, <a href="/A062916/b062916.txt">Table of n, a(n) for n = 1..1000</a>

%H Otto Forster, <a href="http://www.mathematik.uni-muenchen.de/~forster/sw/aribas.html">ARIBAS Interpreter for Arithmetic</a>

%e 2489 and 9842 are both multiples of 19.

%t okQ[n_]:=Module[{idn=IntegerDigits[n],ridn},ridn=Reverse[idn]; Divisible[ FromDigits[ ridn],19] && idn!=ridn]; Select[19*Range[1000],okQ] (* _Harvey P. Dale_, Dec 03 2011 *)

%t Select[19 Range[1000],!PalindromeQ[#]&&Divisible[IntegerReverse[#],19]&] (* _Harvey P. Dale_, Sep 20 2021 *)

%o (ARIBAS) Programs for A062916 etc: If "m <> rev and" is deleted in line 8, one obtains the sequences which include palindromes (e.g., A062907).

%o (ARIBAS) function A0629xy(n,stop: integer); var m,rev: integer; begin m := n; while m < stop do rev := int_reverse(m); if m <> rev and rev mod n = 0 then write(m," "); end; inc(m,n); end; end;

%o (PARI) Palin(x)= { if (x==0, return(1)); if (x==10, return(0)); y=z=x; ds=ceil(log(x)/log(10)); t=10^(ds - 1); for (i=1, ds\2, d=y-10*(y\10); y\=10; e=z\t; z-=t*e; t/=10; if (e!=d, return(0)) ); return(1) }

%o { default(realprecision, 50); n=0; forstep (m=0, 10^9, 19, if (Palin(m), next); x=m; r=0; while (x>0, d=x-10*(x\10); x\=10; r=r*10 + d); if (r%19 == 0, write("b062916.txt", n++, " ", m); if (n==1000, break)) ) } \\ _Harry J. Smith_, Aug 12 2009

%K nonn,base,easy

%O 1,1

%A _Amarnath Murthy_, Jul 01 2001

%E More terms from _Klaus Brockhaus_, Jul 02 2001