A036447
Double and reverse digits.
Original entry on oeis.org
1, 2, 4, 8, 61, 221, 244, 884, 8671, 24371, 24784, 86594, 881371, 2472671, 2435494, 8890784, 86518771, 245730371, 247064194, 883821494, 8892467671, 24353948771, 24579870784, 86514795194, 883095920371, 2470481916671, 2433383690494
Offset: 0
The following are parallel families:
A000079 (2^n),
A004094 (2^n reversed),
A028909 (2^n sorted up),
A028910 (2^n sorted down),
A036447 (double and reverse),
A057615 (double and sort up),
A263451 (double and sort down);
A000244 (3^n),
A004167 (3^n reversed),
A321540 (3^n sorted up),
A321539 (3^n sorted down),
A163632 (triple and reverse),
A321542 (triple and sort up),
A321541 (triple and sort down).
-
a036447 n = a036447_list !! n
a036447_list = iterate a004093 1 -- Reinhard Zumkeller, Feb 09 2012
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NestList[ FromDigits[ Reverse[ IntegerDigits[ 2# ] ] ] &, 1, 27 ]
NestList[IntegerReverse[2#]&,1,30] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 18 2017 *)
More terms from Larry Reeves (larryr(AT)acm.org), Mar 31 2000
A163632
Triple and reverse digits.
Original entry on oeis.org
1, 3, 9, 72, 612, 6381, 34191, 375201, 3065211, 3365919, 75779001, 300733722, 661102209, 7266033891, 37610189712, 631965038211, 3364115985981, 34975974329001, 300789229729401, 302881986763209, 726982069546809
Offset: 1
The following are parallel families:
A000079 (2^n),
A004094 (2^n reversed),
A028909 (2^n sorted up),
A028910 (2^n sorted down),
A036447 (double and reverse),
A057615 (double and sort up),
A263451 (double and sort down);
A000244 (3^n),
A004167 (3^n reversed),
A321540 (3^n sorted up),
A321539 (3^n sorted down),
A163632 (triple and reverse),
A321542 (triple and sort up),
A321541 (triple and sort down).
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a[n_] := a[n] = If[n==1, 1, IntegerReverse[3a[n-1]]];
Array[a, 40] (* Jean-François Alcover, Jan 01 2021 *)
A132064
Numbers multiplied by 4 and written backwards.
Original entry on oeis.org
1, 4, 61, 442, 8671, 48643, 275491, 4691011, 44046781, 421781671, 4866217861, 44417846491, 469583176771, 4807072338781, 42155398282291, 461921395126861, 4447050855867481, 42996432430288771, 480551127927589171, 4866530171154022291, 46198061648602166491
Offset: 1
Rachit Agrawal (rachit_agrawal(AT)daiict.ac.in), Oct 30 2007
a(4) = reverse(4*a(3)) = reverse(4*reverse(4*a(2))) = reverse(4*reverse(4*reverse(4*a(1)))) = reverse(4*reverse(4*4)) = reverse(4*61) = reverse(244) = 442
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a:= proc(n) option remember; `if`(n=1, 1,
(s-> parse(cat(s[-i]$i=1..length(s))))(""||(4*a(n-1))))
end:
seq(a(n), n=1..30); # Alois P. Heinz, Apr 09 2015
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NestList[IntegerReverse[4#]&,1,20] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Dec 09 2017 *)
A132078
Multiply previous term by 6 and reverse.
Original entry on oeis.org
1, 6, 63, 873, 8325, 5994, 46953, 817182, 2903094, 46581471, 628884972, 2389033773, 83620243341, 640064127105, 362674830483, 8982898406712, 27204409379835, 10972654622361, 66143772953856, 631327736268693, 8512167146697873, 83278108820037015, 90222029256866994
Offset: 1
Rachit Agrawal (rachit_agrawal(AT)daiict.ac.in), Oct 30 2007
a(4) = reverse(6 * a(3)) = reverse(6 * reverse(6 * a(2))) = reverse(6 * reverse( 6 * reverse(6 * a(1)))) = reverse(6 * reverse(6 * reverse(6))) = reverse(6 * 63) = 873.
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f:=func; a:=[1]; for n in [2..25] do Append(~a,f(a[n-1])); end for; a; // Marius A. Burtea, Jan 03 2020
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Nest[Append[#,IntegerReverse[6*#[[-1]]]]&,{1},22] (* James C. McMahon, Mar 03 2025 *)
Name clarified and terms a(16) and beyond from
Andrew Howroyd, Jan 02 2020
A132113
Multiply previous term by 8 and reverse.
Original entry on oeis.org
1, 8, 46, 863, 4096, 86723, 487396, 8619983, 46895986, 888761573, 4852900117, 63900232883, 460368102115, 296184492863, 4092495749632, 65079956993723, 487949556936025, 28845546953093, 447426573467032, 6526377852149753
Offset: 1
Rachit Agrawal (rachit_agrawal(AT)daiict.ac.in), Oct 31 2007
a(4) = reverse(8 * a(3))
= reverse(8 * reverse(8 * a(2)))
= reverse(8 * reverse(8 * reverse(8 * a(1))))
= reverse(8 * reverse(8 * reverse(8)))
= reverse(8 * reverse(8 * 8))
= reverse(8 * 46)
= reverse(368)
= 863.
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rev:=proc(n) local nn: nn:=convert(n,base,10): add(nn[j]*10^(nops(nn)-j), j = 1..nops(nn)) end proc: a[1]:=1: for n from 2 to 20 do a[n]:=rev(8*a[n-1]) end do: seq(a[n],n=1..20); # Definition corrected by Emeric Deutsch, Nov 07 2007
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NestList[IntegerReverse[8#]&,1,20] (* Harvey P. Dale, Dec 22 2018 *)
A132114
Multiply previous term by 7 and reverse.
Original entry on oeis.org
1, 7, 94, 856, 2995, 56902, 413893, 1527982, 47859601, 702710533, 1373798194, 8537856169, 38139946795, 565726979662, 4367588800693, 15840612137503, 125269482488011, 770614773688678, 6470285143034935, 54544210069919254
Offset: 1
Rachit Agrawal (rachit_agrawal(AT)daiict.ac.in), Oct 31 2007
a(4) = reverse(7 * a(3)) = reverse(7 * reverse(7 * a(2))) = reverse(7 * reverse(7 * reverse(7 * a(1)))) = reverse(7 * reverse(7 * reverse(7))) = reverse(7*94) = 856.
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f:=func; a:=[1]; for n in [2..20] do Append(~a,f(a[n-1])); end for; a; // Marius A. Burtea, Jan 03 2020
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seq(n)={my(a=vector(n)); a[1]=1; for(n=2, #a, a[n]=fromdigits(Vecrev(digits(a[n-1]*7)))); a} \\ Andrew Howroyd, Jan 02 2020
A133361
Multiply by 9 and reverse.
Original entry on oeis.org
1, 9, 18, 261, 9432, 88848, 236997, 3792312, 80803143, 782822727, 3454045407, 36680468013, 711212421033, 7929871190046, 41401704886317, 358679343516273, 7546461904118223, 70046073175181976, 487736675856414036, 4236277072800369834, 60582330255639462183
Offset: 1
Rachit Agrawal (rachit_agrawal(AT)daiict.ac.in), Oct 26 2007
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a:= proc(n) option remember; `if`(n=1, 1,
(s-> parse(cat(s[-i]$i=1..length(s))))(""||(9*a(n-1))))
end:
seq(a(n), n=1..25); # Alois P. Heinz, Apr 09 2015
-
a[n_] := a[n] = If[n==1, 1, IntegerReverse[9a[n-1]]];
a /@ Range[40] (* Jean-François Alcover, Jan 01 2021 *)
Showing 1-7 of 7 results.
