The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A132203 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A132203

Number of order-independent ways to represent 24*n+5 as the sum of squares of exactly 5 primes.
(history; published version)

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

AUTHOR

_Jonathan Vos Post (jvospost3(AT)gmail.com) _ and John Sokol (john.sokol(AT)gmail.com), Nov 06 2007

Discussion

Fri Mar 30

18:40

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

#6 by R. J. Mathar at Sun Nov 20 11:27:10 EST 2011

STATUS

editing

approved

#5 by R. J. Mathar at Sun Nov 20 11:27:06 EST 2011

LINKS

T. L. Todorova, D. I. Tolev, <a href="http://arXiv.org/pdfabs/0711.0171">On the distribution of alpha p modulo one for primes p of a special form</a>, Nov 1, 2007.

STATUS

approved

editing

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

KEYWORD

nonn,new

nonn

AUTHOR

Jonathan Vos Post (jvospost2jvospost3(AT)yahoogmail.com) and John Sokol (john.sokol(AT)gmail.com), Nov 06 2007

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

LINKS

T. L. Todorova, D. I. Tolev, <a href="http://arxivarXiv.org/pdf/0711.0171">On the distribution of alpha p modulo one for primes p of a special form</a>, Nov 1, 2007.

KEYWORD

nonn,new

nonn

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

MAPLE

*** please list as 2nd author "John Sokol" <john.sokol@gmail.com> who wrote the "C code + some creative awk and sort unix command line stuff." ***

KEYWORD

nonn,new

nonn

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

NAME

Number of order-independent ways to represent 24*n+5 as the sum of squares of exactly 5 primes.

DATA

0, 0, 0, 1, 1, 2, 1, 2, 2, 3, 3, 3, 2, 4, 3, 5, 3, 5, 6, 5, 6, 6, 5, 8, 6, 9, 6, 7, 10, 8, 9, 9, 8, 10, 8, 11, 8, 8, 13, 11, 10, 11, 11, 14, 10, 14, 13, 9, 17, 13, 12, 15, 13, 17, 11, 15, 17, 10, 17, 17, 14, 17, 16, 19, 12, 17, 19, 13, 18, 17, 14, 17, 17, 23, 16

OFFSET

0,6

COMMENTS

Hua proved in 1938 that every sufficiently large integer n congruent to 5 mod 24 can be written as the sum of the squares of exactly 5 primes.

REFERENCES

L. K. Hua, Some results in the additive prime number theory, Quart J. Math., Oxford, 9 (1938) 68-80.

LINKS

T. L. Todorova, D. I. Tolev, <a href="http://arxiv.org/pdf/0711.0171">On the distribution of alpha p modulo one for primes p of a special form</a>, Nov 1, 2007.

EXAMPLE

a(3) = 1 because the only way, up to permutation, to represent 24*n+5 as the sum of squares of exactly 5 primes is 77 = 5 + 24*3 = 5^2 + 5^2 + 3^2 + 3^2 + 3^2.

a(5) = 2 because 125 = 5 + 24*5 = 5^2 + 5^2 + 5^2 + 5^2 + 5^2 = 7^2 + 7^2 + 3^2 + 3^2 + 3^2.

a(9) = 3 because 221 = 5 + 24*9 = 11^2 + 5^2 + 5^2 + 5^2 + 5^2 = 13^2 + 5^2 + 3^2 + 3^2 + 3^2 = 7^2 + 7^2 + 7^2 + 7^2 + 5^2.

a(13) = 4 because 317 = 5 + 24*13 = 11^2 + 11^2 + 5^2 + 5^2 + 5^2 = 11^2 + 7^2 + 7^2 + 7^2 + 7^2 = 13^2 + 11^2 + 3^2 + 3^2 + 3^2 = 13^2 + 7^2 + 7^2 + 5^2 + 5^2.

a(15) = 5 because 365 = 5 + 24*15 = 11^2 + 11^2 + 7^2 + 7^2 + 5^2 = 13^2 + 11^2 + 5^2 + 5^2 + 5^2 = 13^2 + 13^2 + 3^2 + 3^2 + 3^2 = 13^2 + 7^2 + 7^2 + 7^2 + 7^2 = 17^2 + 7^2 + 3^2 + 3^2 + 3^2.

a(18) = 6 because 437 = 5 + 24*18 = 11^2 + 11^2 + 11^2 + 7^2 + 5^2 = 13^2 + 11^2 + 7^2 +7^2 + 7^2 = 13^2 + 13^2 + 7^2 + 5^2 + 5^2 = 17^2 + 11^2 + 3^2 + 3^2 + 3^2 = 17^2 + 7^2 + 7^2 + 5^2 + 5^2 = 19^2 + 7^2 + 3^2 + 3^2 + 3^2 = 19^2 + 7^2 + 3^2 + 3^2 + 3^2.

a(23) = 8 because 557 = 5 + 24*23 = 13^2 + 11^2 + 11^2 + 11^2 + 5^2 = 13^2 + 13^2 + 11^2 + 7^2 + 7^2 = 13^2 + 13^2 + 13^2 + 5^2 + 5^2 = 17^2 + 11^2 + 7^2 + 7^2 + 7^2 = 17^2 + 13^2 + 7^2 + 5^2 + 5^2 = 19^2 + 11^2 + 5^2 + 5^2 + 5^2 = 19^2 + 13^2 + 3^2 + 3^2 + 3^2 = 19^2 + 7^2 + 7^2 + 7^2 + 7^2.

MAPLE

*** please list as 2nd author "John Sokol" <john.sokol@gmail.com> who wrote the "C code + some creative awk and sort unix command line stuff." ***

KEYWORD

nonn,new

AUTHOR

Jonathan Vos Post (jvospost2(AT)yahoo.com) and John Sokol (john.sokol(AT)gmail.com), Nov 06 2007

STATUS

approved