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 A069743 Let M_n be the n X n matrix M_(i,j)=1/(3^i+3^j), then a(n) is the numerator of det(M_n). 2
 1, 1, 1, 169, 57122, 1130708969104, 60520841316555286464512, 967474236461016996630647788281821986816, 3959258211397422699939531791736812415390620457773645692928 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Curiously, sequence seems related to pentagonal (or 5-gonal) or heptagonal (or 7-gonal) numbers. Some primes follow rules in a(n) factorization. If b(n)= exponent of 13 in a(n) factorization: b(n)=0, 0, 0, 2, 4, 6, 10, 14, 18, 24, 30, 36, 44, 52, 60, 70, 80, 90...so b(3n+1)=A049450(n); b(3n+2)=A049450(n)+2*n; b(3n+3)=A049450(n)+4n. If c(n)= exponent of 11 in a(n) factorization: c(n)=4*(0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, ..) so c(5n+1)=4*A000566(n); c(5n+2)=4*(A000566(n)+2n); c(5n+3)=4*(A000566(n)+3n); c(5n+4)=4*(A000566(n)+4n); c(5n+5)=4*(A000566(n)+5n) LINKS PROG (PARI) for(n=1, 15, print1((numerator(matdet(matrix(n, n, i, j, 1/(3^j+3^i))))), ", ")) CROSSREFS Cf. A069742. Sequence in context: A260862 A006051 A069742 * A210087 A135824 A195219 Adjacent sequences:  A069740 A069741 A069742 * A069744 A069745 A069746 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Apr 21 2002 STATUS approved

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Last modified August 17 23:13 EDT 2022. Contains 356204 sequences. (Running on oeis4.)