A340389 Number at the apex of Recamán's triangle of primes and squares with n rows.

0, 3, 9, 59, 1669, 147456, 60924257

Offset: 1

Author

Sean A. Irvine, Apr 24 2021

Keywords

• nonn
• hard
• more

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.

Examples

			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)
		

References

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

Links

• 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)

Crossrefs

Cf. A089237 (primes and squares).

Programs

PARI

see LINKS

Extensions

a(7) from Bert Dobbelaere, May 11 2021