A117429 Semiprime nearest to 5^n. In case of a tie, choose the smaller.

4, 4, 25, 123, 626, 3127, 15623, 78123, 390623, 1953122, 9765627, 48828127, 244140623, 1220703121, 6103515629, 30517578127, 152587890617, 762939453119, 3814697265623, 19073486328122, 95367431640623

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