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A340389 Number at the apex of Recamán's triangle of primes and squares with n rows. 3
0, 3, 9, 59, 1669, 147456, 60924257 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Form a triangle of n rows and place a distinct prime or square at each position such that (apart from the bottom row) every number is the sum of the two numbers below it, and such that the number at the apex is as small as possible.

REFERENCES

Bernardo Recamán, The Bogotá Puzzles, Dover Publications, 2020, Puzzle 3, p. 3.

LINKS

Table of n, a(n) for n=1..7.

M. F. Hasler, A340389: Notes and PARI program, OEIS wiki, Aug 2021.

M. F. Hasler, PARI code for A340389 (extracted from the above wiki page), Aug 16 2021.

Sean A. Irvine, Java program (github)

EXAMPLE

n=3:

    9

   4 5

  1 3 2

.

n=4:

        59

      23  36

    16   7  29

  13   3   4  25

.

n=5 (B. Mehta):

             1669

           576  1093

        383   193   900

     347    36   157   743

  324    23    13   144   599

.

n=6 (_Sean A. Irvine): _

                     147456

                  63487   83969

              33211   30276   53693

          17424   15787   14489   39204

      10853    6571    9216    5273   33931

  10529     324    6247    2969    2304   31627

.

From Bert Dobbelaere, May 11 2021: (Start)

n=7:

                             60924257

                        21861757  39062500

                    7799257  14062500  25000000

               2736757   5062500   9000000  16000000

           914257   1822500   3240000   5760000  10240000

      258157    656100   1166400   2073600   3686400   6553600

  21961    236196    419904    746496   1327104   2359296   4194304

(End)

PROG

(PARI) see LINKS

CROSSREFS

Cf. A089237 (primes and squares).

Sequence in context: A105466 A261244 A018504 * A140812 A202210 A243425

Adjacent sequences:  A340386 A340387 A340388 * A340390 A340391 A340392

KEYWORD

nonn,hard,more

AUTHOR

Sean A. Irvine, Apr 24 2021

EXTENSIONS

a(7) from Bert Dobbelaere, May 11 2021

STATUS

approved

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Last modified January 28 00:57 EST 2022. Contains 350654 sequences. (Running on oeis4.)