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 since 2^0 = 1 is not prime, but 2^1 = 2 is prime. a(2) = 0 since 2^1 + 2^0 = 2 + 1 = 3 is prime. a(3) = 2 since 2^1 + 2^0 + 2^2 = 2 + 1 + 4 = 7 is prime.
findsm(va, n) = {m = 0; ok = 0; vs = vecsort(va); sa = sum(k=1, #va, 2^va[k]); while (!ok, if (! vecsearch(vs, m), ns = sa + 2^m; if (isprime(ns), ok = 1; break);); m++;); m;}
lista(nn) = {va = []; for (n=1, nn, m = findsm(va, n); va = concat(va, m); print1(m, ", "););} \\ Michel Marcus, Sep 26 2015
from sympy import isprime A259630_list, A259630_set, k = [], set(), 0 while len(A259630_list) < 50: n, m = 0,1 k += m while n in A259630_set or not isprime(k): n += 1 k += m m *= 2 A259630_list.append(n) A259630_set.add(n) # Chai Wah Wu, Jun 27 2019
a(3) = 5 since 1 + 2^(2-1) + 2^(3-1) + 2^(5-1) = 10111_2 = 23 is prime. Note that prime(3) = 5 and A080355(3+1) = 23 prime.
Prime@ Select[Range[10^3], PrimeQ[1 + Total@ Array[2^(Prime[#] - 1) &, #]] &] (* Michael De Vlieger, Oct 31 2018 *)
isok(p) = isprime(p) && isprime(1 + sum(k=1, primepi(p), 2^(prime(k)-1))); \\ Michel Marcus, Oct 27 2018
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