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%I #21 Aug 11 2019 14:23:46
%S 4,4,25,123,626,3127,15623,78123,390623,1953122,9765627,48828127,
%T 244140623,1220703121,6103515629,30517578127,152587890617,
%U 762939453119,3814697265623,19073486328122,95367431640623
%N Semiprime nearest to 5^n. In case of a tie, choose the smaller.
%H Robert Israel, <a href="/A117429/b117429.txt">Table of n, a(n) for n = 0..111</a>
%F a(n) = 5^n + A117430(n).
%e a(0) = 4 because 5^0 + 3 = 4 = A001358(1) and no semiprime is closer to 5^0.
%e a(1) = 4 because 5^1 - 1 = 4 = A001358(1) and no semiprime is closer to 5^1.
%e a(2) = 25 because 5^2 + 0 = 25 = A001358(9), no semiprime is closer to 5^2.
%e a(3) = 123 because 5^3 - 2 = 123 = 3 * 41 = A001358(42), no semiprime is closer.
%e a(4) = 626 because 5^4 + 1 = 626 = 2 * 313, no semiprime is closer.
%e a(5) = 3127 because 5^5 + 2 = 3127 = 53 * 59, no semiprime is closer.
%e a(6) = 15623 because 5^6 - 2 = 15623 = 17 * 919, no semiprime is closer.
%e a(7) = 78123 because 5^7 - 2 = 78123 = 3 * 26041, no semiprime is closer.
%e a(8) = 390623 because 5^8 - 2 = 390623 = 73 * 5351, no semiprime is closer.
%e a(9) = 1953122 because 5^9 - 3 = 1953122 = 2 * 976561, no semiprime is closer.
%e a(10) = 9765627 because 5^10 + 2 = 9765627 = 3 * 3255209, no semiprime closer.
%p nsp:= proc(n) uses numtheory; local k;
%p if bigomega(n)=2 then return n fi;
%p for k from 1 do
%p if n-k > 0 and bigomega(n-k)=2 then return n-k fi;
%p if bigomega(n+k)=2 then return n+k fi
%p od
%p end proc:
%p seq(nsp(5^k),k=0..30); # _Robert Israel_, May 03 2018
%t sp1[n_]:=Module[{k=0},While[PrimeOmega[n-k]!=2,k++];n-k]; sp2[n_]:= Module[ {k=1}, While[ PrimeOmega[n+k]!=2,k++];n+k]; Join[{4},Nearest[ {sp1[#], sp2[#]}, #][[1]]&/@(5^Range[20])] (* _Harvey P. Dale_, Aug 11 2019 *)
%Y Cf. A117416 = Semiprime nearest to 3^n, A117405 = Semiprime nearest to 2^n, A117387 = Prime nearest to 2^n.
%Y Cf. A000079, A001358, A117387, A117405, A117406, A117416, A117430.
%K nonn
%O 0,1
%A _Jonathan Vos Post_, Mar 14 2006
%E Edited by _Robert Israel_, May 03 2018
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