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Triangular numbers that for some k >= 1 are also the sum of the first k odd primes.
1

%I #12 Aug 23 2023 08:35:42

%S 3,15,1236378,1454365,3541791,104856921,2677839153,3656187921870,

%T 3973810409128,1448587865213374600,36691639282445615088081

%N Triangular numbers that for some k >= 1 are also the sum of the first k odd primes.

%C a(n) = A000217(i) = A071148(j) for appropriate i, j.

%e 15 is a term because 15 = 1 + 2 + 3 + 4 + 5 = 3 + 5 + 7.

%t Select[Accumulate[Prime[Range[2, 1000000]]], IntegerQ[Sqrt[8 # + 1]] &]

%o (PARI) lista(nn) = my(s=0); forprime(p=3, nn, s+=p; if(ispolygonal(s, 3), print1(s, ", "))) \\ _Jinyuan Wang_, Aug 10 2023

%Y Intersection of A000217 and A071148.

%Y Cf. A065091, A066527, A364798.

%K nonn,more

%O 1,1

%A _Ilya Gutkovskiy_, Aug 08 2023

%E a(10) from _Jinyuan Wang_, Aug 10 2023

%E a(11) from _Martin Ehrenstein_, Aug 23 2023