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A029966
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Palindromic in bases 10 and 11.
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48
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 232, 343, 454, 565, 676, 787, 898, 909, 26962, 38183, 40504, 49294, 52825, 63936, 75157, 2956592, 2968692, 3262623, 3274723, 3286823, 3298923, 3360633, 3372733, 4348434, 4410144, 4422244, 4581854
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OFFSET
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1,3
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COMMENTS
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The first 79 terms all have an odd number of decimal digits. Is there a term with an even number of decimal digits? - Robert Israel, Nov 23 2014
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LINKS
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MAPLE
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N:= 11: # to get all terms with up to N decimal digits
qpali:= proc(k, b) local L; L:= convert(k, base, b); if L = ListTools:-Reverse(L) then k else NULL fi end proc:
digrev:= proc(k, b) local L, n; L:= convert(k, base, b); n:= nops(L); add(L[i]*b^(n-i), i=1..n); end proc:
Res:= $0..9:
for d from 2 to N do
if d::even then
m:= d/2;
Res:= Res, seq(qpali(n*10^m + digrev(n, 10), 11), n=10^(m-1)..10^m-1);
else
m:= (d-1)/2;
Res:= Res, seq(seq(qpali(n*10^(m+1)+y*10^m+digrev(n, 10), 11), y=0..9), n=10^(m-1)..10^m-1);
fi
od:
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MATHEMATICA
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NextPalindrome[n_] := Block[{l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[idn, Ceiling[l/2]] ]] FromDigits[ Take[idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[idn, Ceiling[l/2]], Reverse[ Take[idn, Floor[l/2]] ]]], idfhn = FromDigits[ Take[idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[idfhn], Drop[ Reverse[ IntegerDigits[idfhn]], Mod[l, 2]] ]]] ]]]; palQ[n_Integer, base_Integer] := Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; l = {0}; a = 0; Do[a = NextPalindrome[a]; If[ palQ[a, 12], AppendTo[l, a]], {n, 100000}]; l (* Robert G. Wilson v, Sep 30 2004 *)
b1=10; b2=11; lst={}; Do[d1=IntegerDigits[n, b1]; d2=IntegerDigits[n, b2]; If[d1==Reverse[d1]&&d2==Reverse[d2], AppendTo[lst, n]], {n, 0, 10000000}]; lst (* Vincenzo Librandi, Nov 23 2014 *)
Select[Range[0, 10^5],
PalindromeQ[#] && # == IntegerReverse[#, 11] &] (* Robert Price, Nov 09 2019 *)
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PROG
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(Magma) [n: n in [0..5000000] | Intseq(n) eq Reverse(Intseq(n))and Intseq(n, 11) eq Reverse(Intseq(n, 11))]; // Vincenzo Librandi, Nov 23 2014
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CROSSREFS
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Cf. A007632, A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029967, A029968, A029969, A029970, A029731, A097855, A099165.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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