A078226 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.
1, 3, 9, 27, 81, 567, 8505, 76545, 9874305, 6763898925, 41672381276925, 25432529276163496725, 6947294789656341278149816125, 2341412581496361870123890149638785410125
Offset: 1
Examples
a(6) = 567 = 7*a(5); the digits alternate odd, even, odd.
Programs
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Maple
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
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Python
A078226_list = [1] for _ in range(20): x = A078226_list[-1] y, x2 = x, 2*x while True: y += x2 s = str(y) for j in range(len(s)-1, -1, -2): if not s[j] in ('1', '3', '5', '7', '9'): break else: for k in range(len(s)-2, -1, -2): if not s[k] in ('0', '2', '4', '6', '8'): break else: A078226_list.append(y) break # Chai Wah Wu, Nov 06 2014
Extensions
More terms from Sascha Kurz, Jan 30 2003
a(12) from R. J. Mathar, Mar 01 2007
a(13), a(14) from Max Alekseyev, May 12 2010