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A131866

Distance of n-th semiprime to nearest square.
(history; published version)

#10 by Harvey P. Dale at Fri Aug 12 12:32:39 EDT 2016

STATUS

editing

approved

#9 by Harvey P. Dale at Fri Aug 12 12:32:33 EDT 2016

LINKS

Harvey P. Dale, <a href="/A131866/b131866.txt">Table of n, a(n) for n = 1..1000</a>

MATHEMATICA

dns[n_]:=Min[n-Floor[Sqrt[n]]^2, Ceiling[Sqrt[n]]^2-n]; dns/@Select[ Range[ 400], PrimeOmega[#]==2&] (* Harvey P. Dale, Aug 12 2016 *)

STATUS

approved

editing

#8 by Russ Cox at Fri Mar 30 18:40:43 EDT 2012

AUTHOR

_Jonathan Vos Post (jvospost3(AT)gmail.com), _, Oct 04 2007

Discussion

Fri Mar 30

18:40

OEIS Server: https://oeis.org/edit/global/228

#7 by Russ Cox at Fri Mar 30 17:39:24 EDT 2012

EXTENSIONS

More terms from _R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, Oct 24 2007

Discussion

Fri Mar 30

17:39

OEIS Server: https://oeis.org/edit/global/190

#6 by N. J. A. Sloane at Sun Jul 11 03:00:00 EDT 2010

EXAMPLE

a(1) = 0 because the 1st first semiprime is 4, which is a square.

KEYWORD

easy,nonn,new

#5 by N. J. A. Sloane at Fri Feb 27 03:00:00 EST 2009

EXAMPLE

a(2) = 2 because the 2nd semiprime is 6, and |6-4| = 2 where 4 is the nearest square to 6.

a(4) = 1 because the 4th semiprime is 10, and |10-9| = 1 where 9 is the nearest square to 10.

KEYWORD

easy,nonn,new

#4 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

easy,nonn,new

AUTHOR

Jonathan Vos Post (jvospost2jvospost3(AT)yahoogmail.com), Oct 04 2007

#3 by N. J. A. Sloane at Sun Jun 29 03:00:00 EDT 2008

FORMULA

a(n)=A053188(A001358(n)) (corrected by Richard R. J. Mathar, Nov 19 2007).

KEYWORD

easy,nonn,new

#2 by N. J. A. Sloane at Sun Dec 09 03:00:00 EST 2007

COMMENTS

For each semiprime, find the closest square (preceding or succeeding); subtract, take absolute value.

FORMULA

A053186(A001358(n)). For each semiprime, find the closest square (preceding or succeeding); subtract, take absolute value.

a(n)=A053188(A001358(n)) (corrected by Richard Mathar, Nov 19 2007).

CROSSREFS

Cf. A001358, A047972, A053186A053188.

#1 by N. J. A. Sloane at Sat Nov 10 03:00:00 EST 2007

NAME

Distance of n-th semiprime to nearest square.

DATA

0, 2, 0, 1, 2, 1, 4, 3, 0, 1, 3, 2, 1, 2, 3, 3, 0, 2, 6, 7, 6, 2, 1, 5, 7, 4, 1, 4, 5, 6, 9, 7, 6, 5, 6, 10, 6, 3, 2, 0, 1, 2, 8, 11, 10, 3, 2, 1, 1, 2, 11, 11, 10, 8, 3, 0, 8, 9, 13, 11, 9, 2, 5, 6, 7, 9, 10, 13, 12, 11, 10, 8, 7, 6, 4, 1, 10, 12, 9, 7, 3, 2, 3, 6, 9, 11, 15, 11, 2, 0, 2, 6, 9, 10, 12

OFFSET

1,2

COMMENTS

This to semiprimes A001358 as A047972 is to primes A000040.

FORMULA

A053186(A001358(n)). For each semiprime, find the closest square (preceding or succeeding); subtract, take absolute value.

EXAMPLE

a(1) = 0 because the 1st semiprime is 4, which is a square.

a(2) = 2 because the 2nd semiprime is 6, and |6-4| = 2 where 4 is the nearest square to 6.

a(3) = 0 because the 3rd semiprime is 9, which is a square.

a(4) = 1 because the 4th semiprime is 10, and |10-9| = 1 where 9 is the nearest square to 10.

CROSSREFS

Cf. A001358, A047972, A053186.

KEYWORD

easy,nonn,new

AUTHOR

Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 04 2007

EXTENSIONS

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 24 2007

STATUS

approved