This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(1) = 1 because 1 is the first odd term in A000027. a(2) = 1 + 3 = 4, the sum of the first two odd terms in A000027, and so on.
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {1, 4, 19, 40, 85, 140}, 50] (* Amiram Eldar, Mar 05 2022 *)
to(n) = (2*n-1)*(2*n-1-(-1)^n)/2; \\ A014493 a(n) = sum(k=1, n, to(k)); \\ Michel Marcus, Mar 05 2022
def A352116(n): return n*((n-1)<<1)*(n+1)//3 + n*(n&1) # Chai Wah Wu, Feb 12 2023
Even triangular numbers 6, 10, 28, 36, 66, and 78 are all followed by a prime number. Even triangular number 120 is followed by a composite number 121. Thus, a(1) = 120.
Select[Table[n (n + 1)/2, {n, 0, 200}], EvenQ[#] && ! PrimeQ[# + 1] &]
Select[Accumulate[Range[0,300]],EvenQ[#]&&!PrimeQ[#+1]&] (* Harvey P. Dale, Mar 23 2025 *)
lista(nn) = for (n=1, nn, my(t=n*(n+1)/2); if (!(t%2) && !isprime(t+1), print1(t, ", "))) \\ Michel Marcus, Jun 16 2021
from sympy import isprime def A014494(n): return (2*n+1)*(2*n+1-(-1)**n)//2 def ok(et): return not isprime(et+1) print(list(filter(ok, (A014494(n) for n in range(90))))) # Michael S. Branicky, Jun 15 2021
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