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Moessner triangle based on primes, A125312

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    Moessner triangle based on primes. +30 1 2, 3, 5, 10, 21, 13, 48, 105, 80, 29, 264, 628, 553, 232, 47, 1736, 4378, 4235, 2059, 543, 73 (list; table; graph;
    Message 1 of 1 , Dec 13, 2006
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      Moessner triangle based on primes. +30
      1

      2, 3, 5, 10, 21, 13, 48, 105, 80, 29, 264, 628, 553, 232, 47, 1736,
      4378, 4235, 2059, 543, 73 (list; table; graph; listen)

      OFFSET 1,1

      COMMENT Row sums are: 2, 8, 44, 262, 1724, 13024... Conjecture: log
      row n-th sum tends to (2n-3) + some unknown fractional part. E.g. log
      1724 = 7.45...while log 13024 = 9.43... Right border = A011756.

      REFERENCES J. H. Conway and Richard K. Guy, "The Book of Numbers",
      Springer-Verlag, 1996, p. 64.

      FORMULA Begin with the primes and circle every (n*(n+1)/2)-th
      prime: 1, 5, 13, 29, 47... = A011756. Following the instructions in
      A125714, take partial sums of the uncircled terms, making this row 2.
      Circle the terms in row 2 one place to the left of row 1 terms. Take
      partial sums of the uncircled terms, continuing with analogous
      procedures for subsequent rows.

      EXAMPLE First few rows of the triangle are:

      2;

      3, 5;

      10, 21, 13;

      48, 105, 80, 29;

      164, 628, 553, 232, 47;

      1736, 4378, 4235, 2059, 543, 73;

      ..

      CROSSREFS Cf. A125714, A125777, A011756.

      KEYWORD nonn,tabl,uned,new

      AUTHOR Gary W. Adamson
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