

A140755


Square array read by rows: T(n,k) = 41*n^2 + k^2 + n*k, with 20 columns.


4



43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421, 461, 167, 172, 179, 188, 199, 212, 227, 244, 263, 284, 307, 332, 359, 388, 419, 452, 487, 524, 563, 604, 373, 379, 387, 397, 409, 423, 439
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OFFSET

1,1


COMMENTS

The original definition of this sequence was obscure: "A prime array is embedded in a binary quadratic equation that is a transform of x^2 x + 41".


LINKS

Table of n, a(n) for n=1..47.


FORMULA

41b^2 + ab + a^2, a = column 1:20, b = row 1:8, factor the row number b starting at b = 2 and remove all prime factors in b (on row 2 just 2's) from all terms on the row. Repeat the process for all rows. The numbers that remain at the end of the process in the 20*8 array will all be prime


EXAMPLE

a = 16, b = 2, S(16,2) = 452, 452/2 = 226, 226/2 = 113 (a prime}
a = 6, b = 3, S(6,3) = 423, 423/3 = 141, 141/3 = 47 (a prime}
a = 6, b = 6, S(6,6) = 1548, 1548/2 = 774, 774/2 = 387, 387/3 = 129,
129/3 = 43 (a prime}


CROSSREFS

Cf. A140754, A140340 (very similar arrays).
Sequence in context: A095503 A095495 A095487 * A095479 A156783 A273595
Adjacent sequences: A140752 A140753 A140754 * A140756 A140757 A140758


KEYWORD

nonn,tabf


AUTHOR

Aldrich Stevens (aldrichstevens(AT)msn.com), May 27 2008


EXTENSIONS

Partially edited with better definition by Omar E. Pol, Jan 11 2009
More terms from Omar E. Pol, Jan 11 2009


STATUS

approved



