## 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
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