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A297645 Hexagonal numbers (A000384) in which parity of digits alternates.

%I A297645 #9 Jan 06 2018 22:27:44
%S A297645 1,6,45,276,325,496,561,630,703,2145,2701,6903,8385,10585,14365,18721,
%T A297645 25878,38503,47278,74305,89676,90525,107416,109278,147696,149878,
%U A297645 210925,254541,303810,345696,349030,383250,454581,527878,561270,674541,705078,709836
%N A297645 Hexagonal numbers (A000384) in which parity of digits alternates.
%C A297645 Intersection of A000384 and A030141. - _Felix Fröhlich_, Jan 03 2018
%H A297645 Robert Israel, <a href="/A297645/b297645.txt">Table of n, a(n) for n = 1..1000</a>
%e A297645 6903 is in the sequence because 6, 9, 0 and 3 have even and odd parity alternately.
%p A297645 filter:= proc(n) local L;
%p A297645   if n < 10 then return true fi;
%p A297645   L:= convert(n, base, 10) mod 2;
%p A297645   not has(L[2..-1]-L[1..-2], 0)
%p A297645 end proc:
%p A297645 select(filter, [seq(n*(2*n-1),n=1..10^4)]); # _Robert Israel_, Jan 05 2018
%o A297645 (PARI)
%o A297645 is_alt(n) = m=n; e=n%10; n\=10; while(n>0, f=n%10; if(e%2==f%2, return, e=f; n\=10)); return(m)
%o A297645 select(is_alt, vector(1000, n, (4*n^2-2*n)/2))
%Y A297645 Cf. A297644, A297646, A297647.
%Y A297645 Cf. A000384, A030141, A030152, A030160, A068882.
%K A297645 nonn,base
%O A297645 1,2
%A A297645 _Colin Barker_, Jan 02 2018