A073924 - OEIS

%I #12 Dec 15 2017 17:35:59

%S 1,2,4,16,128,65536,9007199254740992,73786976294838206464,

%T 205688069665150755269371147819668813122841983204197482918576128

%N Smallest power of 2 that is greater than the previous term such that every partial sum (n>1) is a prime.

%C Next term 2^1752 is too large to include.

%e a(5) is 128 because it is the next power of 2 greater than 16 such that 1 + 2 + 4 + 16 + x is prime.

%t a[1] = 1; a[n_] := Block[{k = a[n - 1] + 1, s = Plus @@ (2^Array[a, n - 1])}, While[ !PrimeQ[s + 2^k], k++ ]; k]; Array[2^a[ # ] &, 9] (* _Robert G. Wilson v_, Jan 31 2006 *)

%Y Cf. A073923.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Aug 19 2002

%E More terms from _Jason Earls_, Sep 03 2002