A068665
a(1) = 3; a(n) = smallest palindromic multiple of a(n-1).
Original entry on oeis.org
3, 6, 66, 858, 6006, 66066, 858858, 222444222, 444888444, 21354645312, 21375999957312, 211643775577346112, 211432343445544343234112, 21354666687999978666645312, 211432554877887788778455234112, 211221333755564778877465557333122112
Offset: 1
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a[1] = 3; a[n_] := a[n] = Block[{k = 2}, While[k*a[n - 1] != ToExpression[ StringReverse[ ToString[k*a[n - 1]]]], k++ ]; k*a[n - 1]]; Table[a[n], {n, 1, 16}]
nxt[n_]:=Module[{k=2},While[k*n!=IntegerReverse[k*n],k++];k*n]; NestList[ nxt,3,15] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 14 2016 *)
A068664
a(1) = 1, a(n) = smallest palindromic multiple of a(n-1).
Original entry on oeis.org
1, 2, 4, 8, 88, 616, 6776, 88088, 616616, 232464232, 21154245112, 232696696232, 21175399357112, 21154245133154245112, 232696696464696696232, 21175399378287399357112, 63386501441764911946714410568336
Offset: 1
A068667 (from a(3) on) and this sequence (from a(6) on) coincide.
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a=1; Print[a]; For[n = 2, n <= 15, n++, {an = a; k = 2; str = ToString[k*an]; rstr = StringReverse[str]; While[str != rstr, {k = k + 1; str = ToString[k*an]; rstr = StringReverse[str]; If[k*an > 10^20, {Print["Too big"]; Abort[]}]}]; a := k*an; Print[k, " ", a];}]
spm[n_]:=Module[{k=2},While[!PalindromeQ[k*n],k++];k*n]; NestList[spm,1,15] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 02 2019 *)
A068666
a(1) = 5; a(n) = smallest palindromic multiple of a(n-1).
Original entry on oeis.org
5, 55, 5005, 55055, 50155105, 5065665605, 50155155155105, 5464353998993534645, 541025148469303964841520145, 513016415223221833242338122322514610315
Offset: 1
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a[1] = 5; a[n_] := a[n] = Block[{k = 2}, While[k*a[n - 1] != ToExpression[ StringReverse[ ToString[k*a[n - 1]]]], k++ ]; k*a[n - 1]]; Table[a[n], {n, 1, 9}]
spm[n_]:=Module[{k=2},While[!PalindromeQ[k*n],k++];k*n]; NestList[spm,5,10] (* Harvey P. Dale, Nov 10 2022 *)
A068667
a(1) = 7; a(n) = smallest palindromic multiple of a(n-1).
Original entry on oeis.org
7, 77, 616, 6776, 88088, 616616, 232464232, 21154245112, 232696696232, 21175399357112, 21154245133154245112, 232696696464696696232, 21175399378287399357112, 63386501441764911946714410568336
Offset: 1
Cf.
A068664 (from a(6) on) and this sequence (from a(3) on) coincide.
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a[1] = 7; a[n_] := a[n] = Block[{k = 2}, While[k*a[n - 1] != ToExpression[ StringReverse[ ToString[k*a[n - 1]]]], k++ ]; k*a[n - 1]]; Table[a[n], {n, 1, 14}]
NestList[Module[{k=2},While[!PalindromeQ[k #],k++];k #]&,7,10] (* The program generates the first 11 terms of the sequence. *) (* Harvey P. Dale, Feb 07 2025 *)
A068971
Multipliers resulting from A068664.
Original entry on oeis.org
2, 2, 2, 11, 7, 11, 13, 7, 377, 91, 11, 91, 999001, 11, 91, 2993402878
Offset: 1
A068972
Multipliers resulting from A068665.
Original entry on oeis.org
2, 11, 13, 7, 11, 13, 259, 2, 48, 1001, 9901, 999001, 101, 9901, 999001, 999001, 999999000001, 100000042609376
Offset: 1
A068973
Multipliers resulting from A068666.
Original entry on oeis.org
11, 91, 11, 911, 101, 9901, 108949, 99009901
Offset: 1
A068668
a(1) = 9; a(n) = smallest palindromic multiple of a(n-1).
Original entry on oeis.org
9, 99, 1881, 171171, 1882881, 306909603, 11355655311, 1033364633301, 1034397997934301, 10241574577547514201, 10231343244544544234313201, 112544775689989986577445211, 1023144555797698967975554413201, 102221350448336861989168633844053122201, 11233003103852144358833233885344125830130033211
Offset: 1
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a[1] = 9; a[n_] := a[n] = Block[{k = 2}, While[k*a[n - 1] != ToExpression[ StringReverse[ ToString[k*a[n - 1]]]], k++ ]; k*a[n - 1]]; Table[a[n], {n, 1, 13}] (* Robert G. Wilson v, Apr 19 2002 *)
A070069
a(1) = 11; a(n) = smallest palindromic multiple of a(n-1).
Original entry on oeis.org
11, 22, 44, 88, 616, 6776, 88088, 616616, 232464232, 21154245112, 232696696232, 21175399357112, 21154245133154245112, 232696696464696696232, 21175399378287399357112, 63386501441764911946714410568336
Offset: 1
Cf.
A068664 (from a(5) on) and this sequence (from a(4) on) coincide.
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e[1] = 11; e[n_] := e[n] = Block[{k = 2}, While[k*e[n - 1] != ToExpression[ StringReverse[ ToString[k*e[n - 1]]]], k++ ]; k*e[n - 1]]; Table[e[n], {n, 1, 12}]
Showing 1-9 of 9 results.