A036058
Summarize digits of preceding number, by decreasing digit value. Start with a(0) = 0.
Original entry on oeis.org
0, 10, 1110, 3110, 132110, 13123110, 23124110, 1413223110, 1423224110, 2413323110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110, 1433223110
Offset: 0
The third term is 1110 because the second term contains one 1 and one 0.
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a(n)=if(n>9,1433223110,[0,10,1110,3110,132110,13123110,23124110,1413223110, 1423224110,2413323110][n+1]) \\ Charles R Greathouse IV, Jul 24 2012
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a(n,a=0)={for(k=1,n,a==(a=A244112(a))&&break);a} \\ M. F. Hasler, Feb 25 2018
A036066
The summarize Lucas sequence: summarize the previous two terms, start with 1, 3.
Original entry on oeis.org
1, 3, 1311, 2331, 331241, 14432231, 34433241, 54533231, 2544632221, 163534435221, 263544436231, 363554634231, 463554733221, 17364544733221, 37263554634231, 37363554734231, 37364544933221, 1937263554933221, 3927263544835231, 391827264534836231, 293827363544836231
Offset: 0
Cf.
A244112 (summarizing as used here: by decreasing digit value),
A047842 (alternative summarizing method: by increasing digit value),
A047843 (another method: don't omit missing digits between smallest and largest one).
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a:= proc(n) option remember; `if`(n<2, 2*n+1, (p-> parse(cat(seq((c->
`if`(c=0, [][], [c, 9-i][]))(coeff(p, x, 9-i)), i=0..9))))(
add(x^i, i=map(x-> convert(x, base, 10)[], [a(n-1),a(n-2)]))))
end:
seq(a(n), n=0..20); # Alois P. Heinz, Jun 18 2022
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a[0] = 1; a[1] = 3; a[n_] := a[n] = FromDigits @ Flatten @ Reverse @ Select[ Transpose @ { DigitCount[a[n-1]] + DigitCount[a[n-2]], Append[ Range[9], 0]}, #[[1]] > 0 &];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Dec 30 2017 *)
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{a=[1,3]; for(n=1,50,a=concat(a,A244112(eval(Str(a[n],a[n+1]))))); a} \\ M. F. Hasler, Feb 25 2018
A036106
A summarize Fibonacci sequence: summarize the previous two terms!.
Original entry on oeis.org
1, 2, 1211, 2231, 133241, 14333231, 24632241, 1634534231, 261544434231, 262564533241, 363564435231, 464544634221, 463574533221, 17363574434221, 37263554634231, 37363554734231, 37364544933221, 1937263554933221
Offset: 0
a(24) = 293847463554538221;
a(25) = 294827365564537221 = first term of first period;
a(26) = 293837366554537221;
a(70) = 294837364554538221 = last term of first period != a(24);
a(71) = 294827365564537221 = a(25) = first term of second period;
a(72) = 293837366554537221 = a(26);
a(116) = 294837364554538221 = a(70) = last term of second period;
a(117) = 294827365564537221 = a(71) = first term of third period.
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import Data.List (sort, group); import Data.Function (on)
a036106 n = a036106_list !! n
a036106_list = 1 : 2 : map (read . concatMap say . reverse . group . sort)
(zipWith ((++) `on` show) a036106_list $ tail a036106_list)
where say ws = (show $ length ws) ++ [head ws]
-- Reinhard Zumkeller, Oct 05 2015
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a[0] = 1; a[1] = 2; a[n_] := a[n] = Reverse /@ (IntegerDigits /@ {a[n-2], a[n-1]} // Flatten // Tally // Sort // Reverse) // Flatten // FromDigits; Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Nov 02 2016 *)
A036067
A summarize Fibonacci sequence starting with a(0)=a(1)=0: summarize the previous two terms!.
Original entry on oeis.org
0, 0, 20, 1220, 321120, 13423120, 1433424120, 4443424120, 8433423120, 187443422120, 28175443523120, 2827255433624120, 282716454443823120, 382726356443923120, 19382736256463823120, 29382756253483823120
Offset: 0
A036103
A look-and-say sequence: each term summarizes the previous two terms.
Original entry on oeis.org
0, 1, 1110, 4110, 145120, 1524124120, 2534425120, 354413624120, 16355433523120, 26454463424120, 36456453523120, 46457443522120, 1736556443522120, 2736556433623120, 2756553463623120, 2766552473622120
Offset: 0
a(26) = 39283736554483723130;
a(27) = 39384726554493622120 = first term of first period;
a(28) = 39383736455493622120;
a(143) = 39283746553473823130 = last term of first period != a(26);
a(144) = 39384726554493622120 = first term of second period = a(27);
a(145) = 39383736455493622120 = a(28).
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import Data.List (sort, group); import Data.Function (on)
a036103 n = a036103_list !! n
a036103_list = 0 : 1 : map (read . concatMap say . group . reverse . sort)
(zipWith ((++) `on` show) a036103_list $ tail a036103_list)
where say w = (show $ length w) ++ [head w]
-- Reinhard Zumkeller, Oct 05 2015
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a[0] = 0; a[1] = 1; a[n_] := a[n] = Reverse /@ (Join[a[n-2] // IntegerDigits, a[n-1] // IntegerDigits] // Tally // SortBy[#, First]& // Reverse) // Flatten // FromDigits;
Array[a, 16, 0] (* Jean-François Alcover, Jul 13 2016 *)
A036109
A summarize Fibonacci sequence: summarize the previous two terms!.
Original entry on oeis.org
2, 1, 1211, 1241, 142251, 15243241, 2534134241, 2554334241, 3564434231, 163564533221, 363544633231, 463534833231, 183625441032221, 2826254473524110, 281726355433825120, 382726554443824120, 482726555453823120, 482726656443822120, 482746555433922120
Offset: 0
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a:= proc(n) option remember; `if`(n<2, 2-n, (p-> parse(cat(seq((c->
`if`(c=0, [][], [c, 9-i][]))(coeff(p, x, 9-i)), i=0..9))))(
add(x^i, i=map(x-> convert(x, base, 10)[], [a(n-1),a(n-2)]))))
end:
seq(a(n), n=0..20); # Alois P. Heinz, Jun 18 2022
A300191
Look and Say the digits of the last three terms, by increasing digit value. Start with a(1)=1, a(2)=2 and a(3)=3.
Original entry on oeis.org
1, 2, 3, 111213, 412223, 51423314, 7152433415, 515253543517, 613263548527, 5142634495263718, 515263549546372819, 516263648566373839, 515283648596374849, 414283649596376859, 3132837475106377869, 10413283746576677869, 20513283644596976859, 30514283545596976859
Offset: 1
1, 2, 3 => there are one '1', one '2' and one '3': 111213;
2, 3, 111213 => there are four '1', two '2' and two '3': 412223;
3, 111213, 412223 => there are five '1', four '2', three '3', one '4': 51423314.
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P:=proc(q) local a,b,c,d,k,n,y,x; y:=array(1..3); x:=array(0..9);
y[1]:=1; y[2]:=2; y[3]:=3;
print(1); print(2); print(3); a:=[]; b:=[1]; c:=[2];
for n from 1 to q do for k from 0 to 9 do x[k]:=0; od;
a:=b; b:=c; c:=convert(y[3],base,10);
for k from 1 to nops(a) do x[a[k]]:=x[a[k]]+1; od;
for k from 1 to nops(b) do x[b[k]]:=x[b[k]]+1; od;
for k from 1 to nops(c) do x[c[k]]:=x[c[k]]+1; od;
y[1]:=y[2]; y[2]:=y[3]; y[3]:=0;
for k from 0 to 9 do if x[k]>0 then if k=0 then d:=10*x[k];
else d:=10*x[k]+k; fi; y[3]:=y[3]*10^(ilog10(d)+1)+d; fi; od;
print(y[3]); od; end: P(10^2);
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Nest[Append[#, FromDigits[Join @@ Map[Flatten@ Reverse@ # &, IntegerDigits@ Sort@ Tally[Join @@ IntegerDigits[#[[-3 ;; -1]]]]]]] &, {1, 2, 3}, 15] (* Michael De Vlieger, Mar 01 2018 *)
A036104
A summarize Fibonacci sequence: summarize the previous two terms!.
Original entry on oeis.org
0, 2, 1210, 222110, 424120, 24523120, 153413522120, 352433624120, 16353453624120, 36354463523120, 46454473423120, 1736357463422120, 3736257453523120, 4736453473623120, 4736454483522120, 183736357463522120
Offset: 0
A036105
A summarize Fibonacci sequence: summarize the previous two terms!.
Original entry on oeis.org
1, 0, 1110, 3120, 13124120, 1423324120, 3433525120, 253453523120, 552463522120, 16652443722120, 1736453423823120, 182736254453724120, 283726355463724120, 284736455453823120, 383736555463722120
Offset: 0
A036107
A summarize Fibonacci sequence: summarize the previous two terms!.
Original entry on oeis.org
1, 4, 1411, 2431, 24131241, 34233241, 44434241, 74433221, 1774333221, 3734534231, 371534733231, 372534932231, 19372524934231, 39272534736231, 3937162534736231, 2947362524935231, 3937363534836231
Offset: 0
Showing 1-10 of 17 results.
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