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A108505 Number of palindromic semiprimes less than 10^n. 1

%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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Last modified November 29 17:22 EST 2023. Contains 367445 sequences. (Running on oeis4.)