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A082239
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Infinite table filled by antidiagonals with smallest numbers such that every partial concatenation of a row or a column gives a prime.
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0
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2, 3, 3, 3, 1, 3, 3, 1, 1, 3, 3, 47, 1, 47, 3, 23, 31, 21, 21, 31, 23, 7, 71, 171, 53, 171, 71, 7, 3, 3, 111, 7, 7, 111, 3, 3, 53, 253, 9, 231, 9, 231, 9, 253, 53, 19, 33, 711, 111, 33, 33, 111, 711, 33, 19, 149, 33, 63, 519, 213, 1, 213, 519, 63, 33, 149, 571, 23, 177, 21, 831, 21, 21, 831, 21, 177, 23, 571, 3, 91, 309
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OFFSET
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1,1
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COMMENTS
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Table is symmetric with respect to its main diagonal.
Like magic squares one can define primagic squares as a symmetric square table of numbers in which every partial concatenation of a row or column gives only primes. 2, 2 3 2 3 3 3 1, 3 1 1 3 1 1, ... are primagic squares of order 1 2 and 3 respectively occurring in the above array. An absolute primagic square can be defined as the one whose members are all prime. A strictly primagic square can be defined as the one in which both the diagonals also yield primes. The primagic square of order 3 above is an example.
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LINKS
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EXAMPLE
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The table starts with
2 3 3 3 3 ...
3 1 1 47 ...
3 1 1 21 ...
3 47 21 ...
3 ...
...
The first row/column gives primes 2, 23, 233, 2333, 23333, ..., while the fourth row/column gives primes 3, 347, 34721, 3472153, ...
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PROG
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(PARI) n=20; M=matrix(n, n); for(s=2, n+1, for(j=1, s-1, i=s-j; M[i, j]=1; while( !ispseudoprime( eval(concat(vector(i, k, Str(M[k, j])))) ) || !ispseudoprime( eval(concat(vector(j, k, Str(M[i, k])))) ), M[i, j]++); print1(M[i, j], ", "); )) /* Max Alekseyev */
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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