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.
For these k, A110299(k) is 2, 7, 19, 101, 3727, 481577, 7706203, 986404613, ... all prime.
isok(k) = isprime(fromdigits(primes(k), 2));
a(4)=26 because 4*prime(1)+2*prime(2)+prime(3)+prime(4) = 8+6+5+7 = 26.
[n eq 1 select 2 else 2*Self(n-1)+NthPrime(n)-NthPrime(n-1):n in [1..31]]; // Marius A. Burtea, Oct 17 2019
a[1]:=2: for n from 2 to 35 do a[n]:=2*a[n-1]+ithprime(n)-ithprime(n-1) od: seq(a[n],n=1..35);
a[1] = 2; a[n_] := 2*a[n - 1] + Prime[n] - Prime[n - 1]; Table[a[n], {n, 1, 31}] (* James C. McMahon, Dec 10 2023 *)
FoldList[10 #1 + Prime@ #2 &, 0, Range@ 17] (* Michael De Vlieger, May 24 2017 *)
a(n) = fromdigits(primes(n)); \\ Kevin Ryde, Jun 22 2022
from sympy import prime
l = [0]
for i in range(20):
l += [10 * l[i] + prime(i + 1)]
print(l) # Indranil Ghosh, May 25 2017
Table[Sum[2^(i-2) * Prime[i], {i, 1, n}], {n, 1, 10}] (* G. C. Greubel, Oct 15 2016 *)
Accumulate[Table[Prime[i]*2^(i-2),{i,30}]] (* Harvey P. Dale, Aug 14 2019 *)
a(n) = sum(k=1, n, prime(k)*2^(k-2)); \\ Michel Marcus, Oct 15 2016
5 is prime, so a(6) = 2*a(5) = 2*9 = 18. 6 is not prime, so a(7) = a(6) + 1 = 18 + 1 = 19.
a[0] = 0; a[n_] := a[n] = If[PrimeQ[n - 1], 2*a[n - 1], a[n - 1] + 1]; Array[a, 50, 0] (* Amiram Eldar, Jun 21 2022 *)
a(n) = my(k=primepi(n-1)); fromdigits(primes(k),2) - 1<Kevin Ryde, Jun 22 2022
from sympy import isprime a = [0]; [a.append(2*a[-1] if isprime(n) else a[-1]+1) for n in range(48)] print(a) # Michael S. Branicky, Jun 21 2022
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