A073924
Smallest power of 2 that is greater than the previous term such that every partial sum (n>1) is a prime.
Original entry on oeis.org
1, 2, 4, 16, 128, 65536, 9007199254740992, 73786976294838206464, 205688069665150755269371147819668813122841983204197482918576128
Offset: 1
a(5) is 128 because it is the next power of 2 greater than 16 such that 1 + 2 + 4 + 16 + x is prime.
-
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 *)
A073925
Powers of 2 rearranged such that every partial sum (n>1) is composite.
Original entry on oeis.org
1, 8, 16, 2, 64, 4, 256, 1024, 32, 128, 512, 2048, 8192, 4096, 16384, 32768, 131072, 65536, 2097152, 262144, 524288, 1048576, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 2147483648, 1073741824
Offset: 1
a(2)=8 because 1+2=3, 1+4=5 are primes and 1+8=9 is composite.
-
N:= 100: # for terms before the first > 2^N
Cands:= [seq(2^i,i=0..N)]:
Res:= NULL: s:= 0: nC:= N+1:
found:= true;
while found do
found:= false;
for i from 1 to nC do
if not isprime(s+Cands[i]) then
Res:= Res, Cands[i];
s:= s + Cands[i];
Cands:= subsop(i=NULL, Cands);
nC:= nC-1;
found:= true;
break
fi
od
od:
Res; # Robert Israel, Apr 05 2020
A073926
Powers of 2 rearranged so that every partial sum after 1 is a proper prime power.
Original entry on oeis.org
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