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a(1) = 2, a(n+1) is the smallest multiple of a(n) such that the digits are alternately odd and even. The unit digit is always even and parity alternates.
4

%I #14 Aug 07 2015 02:39:25

%S 2,4,8,16,32,96,672,45696,2787456,270383232,507238943232,

%T 27274745216527872,141232121898569036783616,

%U 216567470725252501672125832323072

%N a(1) = 2, a(n+1) is the smallest multiple of a(n) such that the digits are alternately odd and even. The unit digit is always even and parity alternates.

%e a(7) = 672 = 7*a(6) = 7*96. Starting with the unit digit the digits in 672 are alternately even and odd.

%p isAltr := proc(n) local nshft,osgn,sgn ; nshft := n ; osgn := ( n mod 10 ) mod 2 ; while nshft >= 10 do nshft := floor(nshft/10) ; sgn := ( nshft mod 10 ) mod 2 ; if sgn = osgn then RETURN(false) ; fi ; osgn := sgn ; od ; RETURN(true) ; end: A078227 := proc(prev) local m; m := 2 ; while true do if isAltr(m*prev) then RETURN(m*prev) ; fi ; m := m+1 ; od ; end: n := 2 : while true do print(n) ; n := A078227(n) : od : # _R. J. Mathar_, Nov 12 2006

%o (Python)

%o A078227_list = [2]

%o for _ in range(20):

%o ....x = A078227_list[-1]

%o ....y = x

%o ....while True:

%o ........y += x

%o ........s = str(y)

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

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

%o ................break

%o ........else:

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

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

%o ....................break

%o ............else:

%o ................A078227_list.append(y)

%o ................break

%o # _Chai Wah Wu_, Nov 06 2014

%Y Cf. A078221, A078222, A078223, A078224, A078225, A078226, A078228.

%K base,more,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 23 2002

%E More terms from _R. J. Mathar_, Nov 12 2006

%E a(13) and a(14) from _Donovan Johnson_, Mar 09 2008