A078226 - OEIS

%I #18 Nov 11 2024 22:27:50

%S 1,3,9,27,81,567,8505,76545,9874305,6763898925,41672381276925,

%T 25432529276163496725,6947294789656341278149816125,

%U 2341412581496361870123890149638785410125

%N a(1) = 1, a(n+1) is the smallest odd multiple of a(n) (other than a(n) itself) in which the digits are alternately even and odd.

%e a(6) = 567 = 7*a(5); the digits alternate odd, even, odd.

%p isA030141 := proc(n) local dgs,i ; dgs := convert(n,base,10) ; for i from 1 to nops(dgs)-1 do if ( op(i,dgs)+op(i+1,dgs)) mod 2 = 0 then RETURN(false) ; fi ; od ; RETURN(true) ; end: A078226 := proc(nmax) local a,f; a := [1] ; while nops(a) < nmax do f := 3 ; while true do if isA030141(f*op(-1,a)) then a := [op(a),f*op(-1,a)] ; print(op(-1,a)) ; break ; fi ; f := f+2 ; od ; od ; end: A078226(13) ; # _R. J. Mathar_, Mar 01 2007

%o (Python)

%o A078226_list = [1]

%o for _ in range(20):

%o     x = A078226_list[-1]

%o     y, x2 = x, 2*x

%o     while True:

%o         y += x2

%o         s = str(y)

%o         for j in range(len(s)-1, -1, -2):

%o             if not s[j] in ('1', '3', '5', '7', '9'):

%o                 break

%o         else:

%o             for k in range(len(s)-2, -1, -2):

%o                 if not s[k] in ('0', '2', '4', '6', '8'):

%o                     break

%o             else:

%o                 A078226_list.append(y)

%o                 break

%o # _Chai Wah Wu_, Nov 06 2014

%Y Cf. A078221, A078222, A078223, A078224, A078225, A078227.

%K base,nonn

%O 1,2

%A _Amarnath Murthy_, Nov 23 2002

%E More terms from _Sascha Kurz_, Jan 30 2003

%E a(12) from _R. J. Mathar_, Mar 01 2007

%E a(13), a(14) from _Max Alekseyev_, May 12 2010