A078221
a(1) = 1, a(n+1) > a(n) is the smallest multiple of a(n) using only odd digits.
Original entry on oeis.org
1, 3, 9, 99, 9999, 99999999, 9999999999999999, 99999999999999999999999999999999, 9999999999999999999999999999999999999999999999999999999999999999
Offset: 1
-
1,3,seq(10^(2^(n-3))-1,n=3..11);
-
def A078221(n): return 2*n-1 if n < 3 else 10**(2**(n-3)) - 1 # Chai Wah Wu, Jan 12 2022
A078223
a(1) = 2, a(n+1) > a(n) is the smallest multiple of a(n) using only even digits but not divisible by 10 (i.e., having no trailing zeros).
Original entry on oeis.org
2, 4, 8, 24, 48, 288, 864, 6048, 260064, 26266464, 40082624064, 866826828008064, 26444286042042008448, 20286626620462624006244884224, 22488068646246262608620204848404846444288, 284860000088022466828484860444044822420060828284646488064
Offset: 1
-
a[n_] := a[n] = Block[{k = 2, b = a[n - 1], c = 2 Range[0, 4]}, While[Mod[k*b,10]==0 || Union@ Join[c, IntegerDigits[k*b]] != c, k++]; k*b]; a[1] = 2; Array[a,14] (* Robert G. Wilson v, May 26 2014 *)
Original entry on oeis.org
2, 2, 3, 2, 6, 3, 7, 43, 101, 1526, 21626, 30507, 767145938, 1108516909537, 12667161621083528
Offset: 1
a(9) = A078223(10) / A078223(9) = 26266464 / 260064 = 101.
Original entry on oeis.org
3, 3, 11, 101, 10001, 100000001, 10000000000000001, 100000000000000000000000000000001, 10000000000000000000000000000000000000000000000000000000000000001
Offset: 1
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.
Original entry on oeis.org
1, 3, 9, 27, 81, 567, 8505, 76545, 9874305, 6763898925, 41672381276925, 25432529276163496725, 6947294789656341278149816125, 2341412581496361870123890149638785410125
Offset: 1
a(6) = 567 = 7*a(5); the digits alternate odd, even, odd.
-
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
-
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
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.
Original entry on oeis.org
2, 4, 8, 16, 32, 96, 672, 45696, 2787456, 270383232, 507238943232, 27274745216527872, 141232121898569036783616, 216567470725252501672125832323072
Offset: 1
a(7) = 672 = 7*a(6) = 7*96. Starting with the unit digit the digits in 672 are alternately even and odd.
-
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
-
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
Original entry on oeis.org
2, 2, 2, 2, 3, 7, 68, 61, 97, 1876, 53771, 5178128, 1533415117
Offset: 1
Original entry on oeis.org
3, 3, 3, 3, 7, 15, 9, 129, 685, 6161, 610297, 273165705, 337025079889
Offset: 1
Original entry on oeis.org
3, 5, 5, 5, 25, 17, 449, 16705, 296065, 146689, 14510394113, 4406881562113
Offset: 1
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