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.
%I A287915 #24 Mar 18 2024 03:02:23
%S A287915 1,2,3,5,9,22,25,28,32,41,99,104,138,183,225,361,641,1636,1719,3191,
%T A287915 3590,4144,5340,6372,6893,6915,8429,10024,10546,16401,21636,22612,
%U A287915 24813,31416,36065
%N A287915 Indices of primes in A007443.
%C A287915 Sequence A007443, the binomial transform of the primes A000040, is defined as A007443(n) = Sum_{k=1..n} binomial(n-1,k-1)*prime(k). This is also the first column of the infinite square array T(m,n) with T(1,n) = prime(n) and T(m+1,n) = T(m,n) + T(m,n+1), as for binomial coefficients. Successive rows result from applying this operation of taking the sum of successive terms. So it would be more natural to use index 0 for the first term of this sequence (which is also the only even term, and results from applying the operation 0 times to the primes). This would yield the sequence 0, 1, 2, 4, 8, 21, 24, 27, 31, 40, 98, 103, 137, 182, ...
%C A287915 The next term, if it exists, is greater than 20000. - _Vaclav Kotesovec_, Dec 19 2020
%C A287915 Any subsequent terms are > 10^5. - _Lucas A. Brown_, Mar 18 2024
%H A287915 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A287915.py">Python program</a>.
%t A287915 A007443 = Table[Sum[Binomial[n-1, k-1]*Prime[k], {k, 1, n}], {n, 1, 1000}]; Select[Range[Length[A007443]], PrimeQ[A007443[[#]]]&] (* _Vaclav Kotesovec_, Dec 19 2020 *)
%o A287915 (PARI) for(n=1,199,isprime(A007443(n))&&print1(n","))
%Y A287915 Cf. A007443.
%K A287915 nonn,hard,more
%O A287915 1,2
%A A287915 _M. F. Hasler_, Jun 02 2017
%E A287915 a(18)-a(22) from _Jinyuan Wang_, Dec 19 2020
%E A287915 a(23)-a(30) from _Vaclav Kotesovec_, Dec 19 2020
%E A287915 a(31)-a(35) from _Lucas A. Brown_, Mar 18 2024