

A117430


Integer k such that 5^n + k = A117429(n).


2



3, 1, 0, 2, 1, 2, 2, 2, 2, 3, 2, 2, 2, 4, 4, 2, 8, 6, 2, 3, 2, 2, 4, 2, 6, 2, 4, 2, 3, 17, 9, 4, 8, 6, 12, 14, 2, 6, 8, 2, 6, 24, 2, 14, 6, 4, 18, 6, 3, 6, 16, 10, 16, 12, 12, 2, 16, 6, 16, 12, 2, 6, 12, 12, 8, 19, 6, 6, 24, 16, 4, 2, 16, 4, 8, 4, 16
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OFFSET

0,1


COMMENTS

(+/) distance from 5^n to the nearest semiprime.
a(0)=3 and a(1)=1 are the only terms == 3 (mod 4), as 5^n + 3 is divisible by 4.  Robert Israel, May 03 2018


LINKS

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


FORMULA

a(n) = Integer k such that 5^n + k = A117429(n). a(n) = A117429(n)  5^n. a(n) = Min{k such that A001358(i) + k = 5^n}.


EXAMPLE

a(0) = 3 because 5^0 + 3 = 4 = A001358(1) and no semiprime is closer to 5^0.
a(1) = 1 because 5^1  1 = 4 = A001358(1) and no semiprime is closer to 5^1.
a(2) = 0 because 5^2 + 0 = 25 = A001358(9), no semiprime is closer to 5^2 [this is the only 0 element].
a(3) = 2 because 5^3  2 = 123 = 3 * 41 = A001358(42), no semiprime is closer.
a(4) = 1 because 5^4 + 1 = 626 = 2 * 313, no semiprime is closer.
a(5) = 2 because 5^5 + 2 = 3127 = 53 * 59, no semiprime is closer.


MAPLE

nsp:= proc(n) uses numtheory; local k;
if bigomega(n)=2 then return n fi;
for k from 1 do
if nk > 0 and bigomega(nk)=2 then return nk fi;
if bigomega(n+k)=2 then return n+k fi
od
end proc:
seq(nsp(5^n)5^n, n=0..30); # Robert Israel, May 03 2018


MATHEMATICA

nsp[n_] := Module[{k}, If[PrimeOmega[n] == 2, Return[n]]; For[k = 1, True, k++, If[nk > 0 && PrimeOmega[nk] == 2, Return[nk]]; If[PrimeOmega[n+k] == 2, Return[n+k]]]];
a[n_] := a[n] = nsp[5^n]  5^n;
Table[Print[n, " ", a[n]]; a[n], {n, 0, 76}] (* JeanFrançois Alcover, Jul 23 2020, after Maple *)


CROSSREFS

Cf. A000079, A001358, A117387, A117405, A117406, A117416, A117429.
Sequence in context: A284826 A307752 A101548 * A143676 A002726 A119734
Adjacent sequences: A117427 A117428 A117429 * A117431 A117432 A117433


KEYWORD

sign


AUTHOR

Jonathan Vos Post, Mar 14 2006


EXTENSIONS

More terms from Robert Israel, May 03 2018


STATUS

approved



