A262962 -id:A262962 - cp's OEIS frontend

A026962 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026626.

1, 6, 24, 108, 406, 1572, 5961, 22788, 87209, 335010, 1290376, 4983162, 19286891, 74797176, 290586771, 1130716508, 4406049037, 17191077082, 67152699384, 262594530318, 1027851765350, 4026831276662, 15788979175102, 61954847930374, 243278117470476, 955907159445522

Offset: 1

Clark Kimberling

nonn

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A026626, A026627, A026628, A026629, A026630, A026631, A026632.
Cf. A026633, A026634, A026635, A026636, A026961, A026963, A026964.
Cf. A026965.

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, If[k==1 || k==n-1, Floor[3*n/2], T[n-1,k-1] +T[n-1,k]]]; (* T = A026626 *)
A262962[n_]:=Sum[T[n,k]*T[n,k+1], {k,0,n-1}];
Table[A262962[n], {n,40}] (* G. C. Greubel, Jun 23 2024 *)

@CachedFunction
def T(n, k): # T = A026626
    if (k==0 or k==n): return 1
    elif (k==1 or k==n-1): return int(3*n//2)
    else: return T(n-1, k-1) + T(n-1, k)
def A262962(n): return sum( T(n,k)*T(n,k+1) for k in range(n))
[A262962(n) for n in range(1,41)] # G. C. Greubel, Jun 23 2024

More terms from Sean A. Irvine, Oct 20 2019

A262098 Primes p such that 2^p + 9 is also prime.

Original entry on oeis.org

2, 3, 5, 7, 23, 37, 47, 263, 317, 3229, 3253

Offset: 1

Vincenzo Librandi, Sep 18 2015

a(12) > 100000. - Dana Jacobsen, Oct 03 2015

a(12) > 382198 using A057196. - Michael S. Branicky, Oct 31 2024

			5 is in sequence because 2^5 + 9 = 41 is prime.

Subsequence of primes of A057196.

Cf. primes p such that 2^p+k is a prime: A057736 (k=3), A175173 (k=5), this sequence (k=9), A155780 (k=11), A175234 (k=15), A262099 (k=17), A175235 (k=21), A175236 (k=23), A262934 (k=27), A262100 (k=29), A262201 (k=33), A262962 (k=35).

[p: p in PrimesUpTo(1000) | IsPrime(2^p+9)];

Select[Prime[Range[1000]], PrimeQ[2^# + 9] &]

for(n=1, 1e3, if(isprime((2^prime(n))+9), print1(prime(n)", "))) \\ Altug Alkan, Sep 18 2015

use ntheory ":all"; use Math::GMP qw/:constant/; forprimes { say if is_prime(2**$+9) } 10000; # _Dana Jacobsen, Oct 03 2015

cp's OEIS Frontend

A026962 a(n) = Sum_{k=0..n-1} T(n,k) * T(n,k+1), with T given by A026626.

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A262098 Primes p such that 2^p + 9 is also prime.

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