A297644 - OEIS

%I #14 Jan 06 2019 03:58:52

%S 1,5,12,70,92,145,210,852,925,2147,2501,3290,3432,3876,4187,4347,6305,

%T 6501,12105,12927,25676,27270,27676,45850,58707,69230,69876,70525,

%U 76501,78547,98945,101270,123410,161212,270725,349692,367290,567030,707610,709672

%N Pentagonal numbers (A000326) in which parity of digits alternates.

%C Intersection of A000326 and A030141. - _Felix Fröhlich_, Jan 03 2018

%H Robert Israel, <a href="/A297644/b297644.txt">Table of n, a(n) for n = 1..2000</a>

%e 3876 is in the sequence because 3, 8, 7 and 6 have odd and even parity alternately.

%p filter:= proc(n) local L;

%p   if n < 10 then return true fi;

%p   L:= convert(n, base, 10) mod 2;

%p   not has(L[2..-1]-L[1..-2], 0)

%p end proc:

%p select(filter, [seq(n*(3*n-1)/2, n=1..1000)]); # _Robert Israel_, Jan 03 2018

%o (PARI)

%o 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 select(is_alt, vector(1000, n, (3*n^2-n)/2))

%Y Cf. A297645, A297646, A297647.

%Y Cf. A000326, A030141, A030152, A030160, A068882.

%K nonn,base

%O 1,2

%A _Colin Barker_, Jan 02 2018