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Revision History for A117430

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Showing entries 1-10 | older changes

A117430

Integer k such that 5^n + k = A117429(n).
(history; published version)

#21 by Peter Luschny at Thu Jul 23 05:02:48 EDT 2020

STATUS

reviewed

approved

#20 by Joerg Arndt at Thu Jul 23 04:50:42 EDT 2020

STATUS

proposed

reviewed

#19 by Jean-François Alcover at Thu Jul 23 03:33:16 EDT 2020

STATUS

editing

proposed

#18 by Jean-François Alcover at Thu Jul 23 03:33:10 EDT 2020

MATHEMATICA

nsp[n_] := Module[{k}, If[PrimeOmega[n] == 2, Return[n]]; For[k = 1, True, k++, If[n-k > 0 && PrimeOmega[n-k] == 2, Return[n-k]]; 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}] (* Jean-François Alcover, Jul 23 2020, after Maple *)

STATUS

approved

editing

#17 by Bruno Berselli at Fri May 04 03:42:17 EDT 2018

STATUS

proposed

approved

#16 by Robert Israel at Thu May 03 21:37:31 EDT 2018

STATUS

editing

proposed

#15 by Robert Israel at Thu May 03 21:37:20 EDT 2018

COMMENTS

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

STATUS

proposed

editing

#14 by Robert Israel at Thu May 03 21:22:58 EDT 2018

STATUS

editing

proposed

#13 by Robert Israel at Thu May 03 21:22:14 EDT 2018

DATA

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

KEYWORD

sign,less,changed

EXTENSIONS

More terms from Robert Israel, May 03 2018

Discussion

Thu May 03

21:22

Robert Israel: Not at all easy (requires some heavy-duty factoring).  And why "less"?

#12 by Robert Israel at Thu May 03 21:17:49 EDT 2018

COMMENTS

Distance from 5^n to the nearest semiprime. See also: A117416 Semiprime nearest to 3^n. A117405 Semiprime nearest to 2^n. A117387 Prime nearest to 2^n.

(+/-) distance from 5^n to the nearest semiprime.

LINKS

Robert Israel, <a href="/A117430/b117430.txt">Table of n, a(n) for n = 0..111</a>

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^n)-5^n, n=0..30); # Robert Israel, May 03 2018

KEYWORD

easy,sign,less

STATUS

approved

editing