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A125312 Moessner triangle based on primes.

%I A125312 #31 Aug 01 2019 09:09:42
%S A125312 2,3,5,10,21,13,48,105,80,29,264,628,553,232,47,1730,4378,4235,2059,
%T A125312 543,73,13024,34620,36078,19553,6063,1095,107,110542,306362,339554,
%U A125312 200769,70350,15166,2000,151,1044900,3003012,3507070,2228398,861305,212514
%N A125312 Moessner triangle based on primes.
%C A125312 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.
%D A125312 J. H. Conway and R. K. Guy, "The Book of Numbers", Springer-Verlag, 1996, p. 64.
%H A125312 Joshua Zucker, <a href="/A125312/b125312.txt">Table of n, a(n) for n = 1..55</a>
%H A125312 G. S. Kazandzidis, <a href="http://www.hms.gr/apothema/?s=sap&amp;i=20">On a conjecture of Moessner and a general problem</a>, Bull. Soc. Math. Grèce (N.S.) 2 (1961), 23-30.
%H A125312 Dexter Kozen and Alexandra Silva, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.120.02.131">On Moessner's theorem</a>, Amer. Math. Monthly 120(2) (2013), 131-139.
%H A125312 R. Krebbers, L. Parlant, and A. Silva, <a href="https://doi.org/10.1007/978-3-319-30734-3_21">Moessner's theorem: an exercise in coinductive reasoning in Coq</a>,  Theory and practice of formal methods, 309-324, Lecture Notes in Comput. Sci., 9660, Springer, 2016.
%H A125312 Calvin T. Long, <a href="https://doi.org/10.2307/3615513">Strike it out--add it up</a>, Math. Gaz. 66 (438) (1982), 273-277.
%H A125312 Alfred Moessner, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1951_0029.pdf">Eine Bemerkung über die Potenzen der natürlichen Zahlen</a>, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 29, 1951.
%H A125312 Ivan Paasche, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1952_0001-0005.pdf">Ein neuer Beweis des Moessnerschen Satzes</a> S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. 1952 (1952), 1-5 (1953). [Two years are listed at the beginning of the journal issue.]
%H A125312 Ivan Paasche, <a href="https://doi.org/10.1007/BF01900739">Beweis des Moessnerschen Satzes mittels linearer Transformationen</a>, Arch. Math. (Basel) 6 (1955), 194-199.
%H A125312 Ivan Paasche, <a href="http://www.numdam.org/article/CM_1954-1956__12__263_0.pdf">Eine Verallgemeinerung des Moessnerschen Satzes</a>, Compositio Math. 12 (1956), 263-270.
%H A125312 Hans Salié, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1952_0007-0011.pdf">Bemerkung zu einem Satz von A. Moessner</a>, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. 1952 (1952), 7-11 (1953). [Two years are listed at the beginning of the journal issue.]
%H A125312 Oskar Perron, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1951_0031-0034.pdf">Beweis des Moessnerschen Satzes</a>, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 31-34, 1951.
%F A125312 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.
%e A125312 First few rows of the triangle are:
%e A125312      2;
%e A125312      3,    5;
%e A125312     10,   21,   13;
%e A125312     48,  105,   80,   29;
%e A125312    164,  628,  553,  232,  47;
%e A125312   1736, 4378, 4235, 2059, 543, 73;
%e A125312   ...
%Y A125312 Cf. A125714, A125777, A011756.
%K A125312 nonn,tabl
%O A125312 1,1
%A A125312 _Gary W. Adamson_, Dec 10 2006
%E A125312 Corrected and extended by _Joshua Zucker_, Jun 17 2007