A078227 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.
2, 4, 8, 16, 32, 96, 672, 45696, 2787456, 270383232, 507238943232, 27274745216527872, 141232121898569036783616, 216567470725252501672125832323072
Offset: 1
Examples
a(7) = 672 = 7*a(6) = 7*96. Starting with the unit digit the digits in 672 are alternately even and odd.
Programs
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Maple
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
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Python
A078227_list = [2] for _ in range(20): x = A078227_list[-1] y = x while True: y += x s = str(y) for j in range(len(s)-1,-1,-2): if not s[j] in ('0','2','4','6','8'): break else: for k in range(len(s)-2,-1,-2): if not s[k] in ('1','3','5','7','9'): break else: A078227_list.append(y) break # Chai Wah Wu, Nov 06 2014
Extensions
More terms from R. J. Mathar, Nov 12 2006
a(13) and a(14) from Donovan Johnson, Mar 09 2008