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A117429 Semiprime nearest to 5^n. In case of a tie, choose the smaller. 2
4, 4, 25, 123, 626, 3127, 15623, 78123, 390623, 1953122, 9765627, 48828127, 244140623, 1220703121, 6103515629, 30517578127, 152587890617, 762939453119, 3814697265623, 19073486328122, 95367431640623 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Robert Israel, Table of n, a(n) for n = 0..111

FORMULA

a(n) = 5^n + A117430(n).

EXAMPLE

a(0) = 4 because 5^0 + 3 = 4 = A001358(1) and no semiprime is closer to 5^0.

a(1) = 4 because 5^1 - 1 = 4 = A001358(1) and no semiprime is closer to 5^1.

a(2) = 25 because 5^2 + 0 = 25 = A001358(9), no semiprime is closer to 5^2.

a(3) = 123 because 5^3 - 2 = 123 = 3 * 41 = A001358(42), no semiprime is closer.

a(4) = 626 because 5^4 + 1 = 626 = 2 * 313, no semiprime is closer.

a(5) = 3127 because 5^5 + 2 = 3127 = 53 * 59, no semiprime is closer.

a(6) = 15623 because 5^6 - 2 = 15623 = 17 * 919, no semiprime is closer.

a(7) = 78123 because 5^7 - 2 = 78123 = 3 * 26041, no semiprime is closer.

a(8) = 390623 because 5^8 - 2 = 390623 = 73 * 5351, no semiprime is closer.

a(9) = 1953122 because 5^9 - 3 = 1953122 = 2 * 976561, no semiprime is closer.

a(10) = 9765627 because 5^10 + 2 = 9765627 = 3 * 3255209, no semiprime closer.

MAPLE

nsp:= proc(n) uses numtheory; local k;

  if bigomega(n)=2 then return n fi;

  for k from 1 do

    if n-k > 0 and bigomega(n-k)=2 then return n-k fi;

    if bigomega(n+k)=2 then return n+k fi

  od

end proc:

seq(nsp(5^k), k=0..30); # Robert Israel, May 03 2018

MATHEMATICA

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 *)

CROSSREFS

Cf. A117416 = Semiprime nearest to 3^n, A117405 = Semiprime nearest to 2^n, A117387 = Prime nearest to 2^n.

Cf. A000079, A001358, A117387, A117405, A117406, A117416, A117430.

Sequence in context: A307552 A171633 A221276 * A132650 A112953 A110139

Adjacent sequences:  A117426 A117427 A117428 * A117430 A117431 A117432

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Mar 14 2006

EXTENSIONS

Edited by Robert Israel, May 03 2018

STATUS

approved

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Last modified December 3 11:03 EST 2020. Contains 338900 sequences. (Running on oeis4.)