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 A188536 Potential magic constants of 7 X 7 magic squares composed of consecutive primes. 4
 797, 1077, 1651, 1691, 1895, 2059, 2817, 3263, 4193, 4615, 4803, 4987, 5453, 5501, 5745, 5993, 6427, 6761, 7149, 7547, 7797, 7943, 8489, 8705, 9439, 9747, 9899, 10201, 10347, 10661, 11059, 12367, 12591, 12815, 13095, 13861, 14359, 14693 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For a 7 X 7 magic square composed of 49 consecutive primes, it is necessary that the sum of these primes is a multiple of 7. This sequence consists of integers equal to the sum of 49 consecutive primes divided by 7. It is not known whether each such set of consecutive primes can be arranged into a 7 X 7 magic square but it looks plausible. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 Natalia Makarova, Order 7 magic squares, which consist of sequential primes (in Russian) EXAMPLE a(2) = 1077: [ 281 167 101 43 191 37 257 173 79 227 71 179 211 137 157 109 139 277 47 251 97 199 151 41 89 223 193 181 83 197 239 229 107 163 59 53 103 263 127 269 149 113 131 271 67 241 61 73 233 ] . a(3) = 1651: [ 239 349 359 113 127 271 193 109 277 311 293 191 307 163 149 223 281 379 283 197 139 199 233 251 211 373 157 227 367 331 179 137 151 173 313 241 131 103 337 257 229 353 347 107 167 181 269 317 263 ] MAPLE s:= proc(n) option remember; `if`(n=1, add(ithprime(i), i=1..49), ithprime(n+48) -ithprime(n-1) +s(n-1)) end: a:= proc(n) option remember; local k, m; a(n-1); for k from 1+b(n-1) while irem(s(k), 7, 'm')<>0 do od; b(n):= k; m end: a(0):=0: b(0):=0: seq(a(n), n=1..50); # Alois P. Heinz, Apr 07 2011 MATHEMATICA Total[#]/7&/@Select[Partition[Prime[Range[400]], 49, 1], Divisible[ Total[ #], 7]&] (* Harvey P. Dale, Jan 03 2012 *) CROSSREFS Cf. A173981, A176571, A177434. Sequence in context: A336943 A108251 A108252 * A252346 A256026 A200201 Adjacent sequences: A188533 A188534 A188535 * A188537 A188538 A188539 KEYWORD nonn AUTHOR Natalia Makarova, Apr 03 2011 EXTENSIONS Edited by Max Alekseyev, Jun 18 2011 STATUS approved

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Last modified December 1 22:24 EST 2023. Contains 367502 sequences. (Running on oeis4.)