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%I #49 Oct 04 2021 21:43:21
%S 0,3,9,59,1669,147456,60924257
%N Number at the apex of Recamán's triangle of primes and squares with n rows.
%C 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.
%D Bernardo Recamán, The Bogotá Puzzles, Dover Publications, 2020, Puzzle 3, p. 3.
%H M. F. Hasler, <a href="https://oeis.org/wiki/User:M._F._Hasler/A340389">A340389: Notes and PARI program</a>, OEIS wiki, Aug 2021.
%H M. F. Hasler, <a href="/A340389/a340389.txt">PARI code for A340389</a> (extracted from the above wiki page), Aug 16 2021.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a340/A340389.java">Java program</a> (github)
%e n=3:
%e 9
%e 4 5
%e 1 3 2
%e .
%e n=4:
%e 59
%e 23 36
%e 16 7 29
%e 13 3 4 25
%e .
%e n=5 (B. Mehta):
%e 1669
%e 576 1093
%e 383 193 900
%e 347 36 157 743
%e 324 23 13 144 599
%e .
%e n=6 (_Sean A. Irvine): _
%e 147456
%e 63487 83969
%e 33211 30276 53693
%e 17424 15787 14489 39204
%e 10853 6571 9216 5273 33931
%e 10529 324 6247 2969 2304 31627
%e .
%e From _Bert Dobbelaere_, May 11 2021: (Start)
%e n=7:
%e 60924257
%e 21861757 39062500
%e 7799257 14062500 25000000
%e 2736757 5062500 9000000 16000000
%e 914257 1822500 3240000 5760000 10240000
%e 258157 656100 1166400 2073600 3686400 6553600
%e 21961 236196 419904 746496 1327104 2359296 4194304
%e (End)
%o (PARI) see LINKS
%Y Cf. A089237 (primes and squares).
%K nonn,hard,more
%O 1,2
%A _Sean A. Irvine_, Apr 24 2021
%E a(7) from _Bert Dobbelaere_, May 11 2021