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A125312 Moessner triangle based on primes. 1
2, 3, 5, 10, 21, 13, 48, 105, 80, 29, 264, 628, 553, 232, 47, 1730, 4378, 4235, 2059, 543, 73, 13024, 34620, 36078, 19553, 6063, 1095, 107, 110542, 306362, 339554, 200769, 70350, 15166, 2000, 151, 1044900, 3003012, 3507070, 2228398, 861305, 212514 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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 R. K. Guy, "The Book of Numbers", Springer-Verlag, 1996, p. 64.

LINKS

Joshua Zucker, Table of n, a(n) for n = 1..55

G. S. Kazandzidis, On a conjecture of Moessner and a general problem, Bull. Soc. Math. Grèce (N.S.) 2 (1961), 23-30.

Dexter Kozen and Alexandra Silva, On Moessner's theorem, Amer. Math. Monthly 120(2) (2013), 131-139.

R. Krebbers, L. Parlant, and A. Silva, Moessner's theorem: an exercise in coinductive reasoning in Coq,  Theory and practice of formal methods, 309-324, Lecture Notes in Comput. Sci., 9660, Springer, 2016.

Calvin T. Long, Strike it out--add it up, Math. Gaz. 66 (438) (1982), 273-277.

Alfred Moessner, Eine Bemerkung über die Potenzen der natürlichen Zahlen, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 29, 1951.

Ivan Paasche, Ein neuer Beweis des Moessnerschen Satzes S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. 1952 (1952), 1-5 (1953). [Two years are listed at the beginning of the journal issue.]

Ivan Paasche, Beweis des Moessnerschen Satzes mittels linearer Transformationen, Arch. Math. (Basel) 6 (1955), 194-199.

Ivan Paasche, Eine Verallgemeinerung des Moessnerschen Satzes, Compositio Math. 12 (1956), 263-270.

Hans Salié, Bemerkung zu einem Satz von A. Moessner, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss. 1952 (1952), 7-11 (1953). [Two years are listed at the beginning of the journal issue.]

Oskar Perron, Beweis des Moessnerschen Satzes, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 31-34, 1951.

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.

Sequence in context: A257113 A076834 A023170 * A300550 A014626 A132418

Adjacent sequences:  A125309 A125310 A125311 * A125313 A125314 A125315

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Dec 10 2006

EXTENSIONS

Corrected and extended by Joshua Zucker, Jun 17 2007

STATUS

approved

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Last modified October 1 17:45 EDT 2020. Contains 337444 sequences. (Running on oeis4.)