A287915 Indices of primes in A007443.

1, 2, 3, 5, 9, 22, 25, 28, 32, 41, 99, 104, 138, 183, 225, 361, 641, 1636, 1719, 3191, 3590, 4144, 5340, 6372, 6893, 6915, 8429, 10024, 10546, 16401, 21636, 22612, 24813, 31416, 36065

Offset

1,2

Comments

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, ...

The next term, if it exists, is greater than 20000. - Vaclav Kotesovec, Dec 19 2020

Any subsequent terms are > 10^5. - Lucas A. Brown, Mar 18 2024

Links

Table of n, a(n) for n=1..35.

Lucas A. Brown, Python program.

Mathematica

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 *)

Prog

(PARI) for(n=1, 199, isprime(A007443(n))&&print1(n", "))

Crossrefs

Cf. A007443.

Sequence in context: A101581 A365044 A349676 * A354141 A105180 A094206

Adjacent sequences: A287912 A287913 A287914 * A287916 A287917 A287918

Keyword

nonn,hard,more

Author

M. F. Hasler, Jun 02 2017

Extensions

a(18)-a(22) from Jinyuan Wang, Dec 19 2020

a(23)-a(30) from Vaclav Kotesovec, Dec 19 2020

a(31)-a(35) from Lucas A. Brown, Mar 18 2024

Status

approved