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A143014
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a(1) = 1. a(n) = the smallest multiple of a(n-1), a(n) > a(n-1), such that a(n) in binary is a palindrome.
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3
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1, 3, 9, 27, 189, 2457, 12285, 159705, 9103185, 2030010255, 11000625571845, 187010634721365, 45069562967848965, 188943190838905598464005, 3169167002067055110614170009605, 53875839035139936880440890163285
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OFFSET
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1,2
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COMMENTS
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All terms are odd.
There are an infinite number of terms. Proof: (2^m + 1)*a(n) is a palindrome, where m is >= the number of binary digits in a(n). So a(n+1) <= (2^m + 1)*a(n).
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LINKS
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MAPLE
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isA006995 := proc(n) local dgs, i ; dgs := convert(n, base, 2) ; for i from 1 to nops(dgs)/2 do if op(i, dgs) <> op(-i, dgs) then RETURN(false) ; fi; od: RETURN(true) ; end: A143014 := proc(n) option remember ; local m, a ; if n = 1 then 1; else for m from 2 do a := m*A143014(n-1) ; if isA006995(a) then RETURN(a) ; fi; od: fi ; end: for n from 1 to 100 do printf("%d, ", A143014(n)) ; od: # R. J. Mathar, Aug 08 2008
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MATHEMATICA
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Fold[Function[{a, n}, Append[a, SelectFirst[Range[2^(n + 2)] Last[a], And[# > Last[a], PalindromeQ[IntegerDigits[#, 2]]] &]]] @@ {#1, #2} &, {1}, Range[2, 13]] (* Michael De Vlieger, Oct 25 2017 *)
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PROG
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(PARI) isok(ka) = my(b=binary(ka)); b==Vecrev(b);
lista(nn) = {print1(a=1, ", "); for (n=2, nn, k=2; while (! isok(k*a), k++); a *= k; print1(k, ", "); ); } \\ Michel Marcus, Oct 26 2017
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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