login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A177434 The magic constants of 6 X 6 magic squares composed of consecutive primes. 7
484, 744, 806, 868, 930, 1390, 1460, 1494, 1634, 1704, 1740, 1848, 1992, 2100, 2172, 2316, 2390, 2540, 3116, 3192, 3694, 3734, 3774, 4486, 4946, 4988, 5736, 6104, 6148, 6526, 6568, 6610, 6776, 6820, 6950, 7036, 7078, 7120, 7984, 8118, 8162, 8828, 9318 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Let Z be a sum of 36 consecutive primes. A necessary condition to get a 6 X 6 magic square using these primes is that Z=6S, where S is even. The smallest magic constant of a 6 X 6 magic square of consecutive primes is 484 (cf. A073520).
Each of the first 100 possible arrays of 36 consecutive primes which satisfy the necessary condition produces a magic square.
A program written by Stefano Tognon was used.
LINKS
FORMULA
a(n) = Sum_{k=0..35} A000040(A000720(A272387(n))+k)/6. - M. F. Hasler, Oct 28 2018
EXAMPLE
S = 744
[139 113 151 131 83 127]
[223 149 89 47 157 79]
[173 103 181 167 59 61]
[ 67 137 53 97 211 179]
[101 199 73 109 71 191]
[ 41 43 197 193 163 107]
S = 806
[131 53 107 157 191 167]
[ 89 229 179 97 109 103]
[ 83 211 71 139 79 223]
[113 101 137 181 227 47]
[197 61 163 59 127 199]
[193 151 149 173 73 67]
S = 868
[191 137 79 193 197 71]
[ 67 157 73 229 239 103]
[179 173 167 97 101 151]
[211 181 223 61 109 83]
[113 131 199 139 59 227]
[107 89 127 149 163 233]
Magic square with S=930 can be pan-diagonal (cf. A073523).
Example of a non-pan-diagonal square:
S = 930
[167 71 151 199 131 211]
[ 89 241 181 73 113 233]
[ 83 227 127 197 229 67]
[239 137 139 103 163 149]
[179 97 223 251 101 79]
[173 157 109 107 193 191]
PROG
(PARI) A177434(n, p=A272387[n], N=6)=sum(i=2, N^2, p=nextprime(p+1), p)/N \\ Uses a precomputed array A272387, but can actually be used to find the terms, cf A272387. - M. F. Hasler, Oct 28 2018
CROSSREFS
Cf. A173981 (analog for 4 X 4), A176571 (analog for 5 X 5), A073523 (36 consecutive primes of a pandiagonal magic square), A073520 (smallest magic sum for n X n), A259733 (most-perfect 8 X 8), A272387 (smallest element of 6 X 6 magic squares of consecutive primes).
Sequence in context: A288082 A251625 A156646 * A202444 A329872 A199330
KEYWORD
nonn
AUTHOR
Natalia Makarova, May 08 2010
EXTENSIONS
Edited by M. F. Hasler, Oct 28 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 29 03:21 EDT 2023. Contains 365749 sequences. (Running on oeis4.)