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%I #4 Mar 30 2012 17:34:55
%S 0,3,7,36,50,269,367,2181,2816,18391,23617,160773,203733,1429749,
%T 1788486,12808711,15889727
%N Number of palindromic semiprimes less than 10^n.
%C Does the limit n-> inf. a(n+2)/a(n) =~ 8*Pi^2/9?
%t 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]]]] ]]]]; fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; c = np = 0; Do[ While[np < 10^n, If[ fQ[np], c++ ]; np = NextPalindrome[np]]; Print[c], {n, 0, 12}]
%Y Cf. A046328.
%K base,nonn
%O 0,2
%A _Robert G. Wilson v_, Jun 06 2005
%E a(15)-a(16) from _Donovan Johnson_, Mar 14 2010
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