A281257 Primes in A067894: primes in the partial sums of the binary representations of the first m natural numbers, reading these representations in decimal.

11, 223, 2556997, 3333331, 14559007, 47836783, 56672227, 65555671, 181114559, 411488881, 583227779, 1399999987, 5723503439, 10047846871, 11361255547, 13787777879, 18474111311, 19905449987, 20235780199, 21226777753, 22557892319, 71445725647, 83447001413, 103459003423

Offset: 1

Author

K. D. Bajpai, Jan 18 2017

Keywords

• nonn
• base

Comments

Intersection of A000040 and A067894.

Examples

			0 + 1 + 10 = 11 (prime), so 11 is in the sequence.
0 + 1 + 10 + 11 + 100 + 101 = 223 (prime), so 223 is in the sequence.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A007088, A067894.

Programs

Maple

select(isprime, ListTools:-PartialSums(map(convert,[$1..1000],binary))); # Robert Israel, Jan 18 2017

Mathematica

Select[Accumulate[Table[FromDigits[IntegerDigits[n, 2]], {n, 0, 1000}]], PrimeQ]

PARI

F(k,{b=10})=sum(i=1,k,subst(Pol(binary(i),y),y,b));
test(k,{b=10})={my(z=F(k,b));return(isprime(z)*z)};
Values(n,{b=10})={my(L=List(),j,t);while(#LR. J. Cano, Jan 19 2017