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

1,1

Comments

Intersection of A000040 and A067894.

Links

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

Example

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.

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]

Prog

(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(#L<n, t=test(j++, b); if(t, listput(L, j))); return(vector(#L, i, L[i]))}
firstTerms(n, {b=10})={my(w=Values(n, b)); return(vector(#w, i, F(w[i], b)))} \\ Example: print(firstTerms(25)); - R. J. Cano, Jan 19 2017

Crossrefs

Cf. A000040, A007088, A067894.

Sequence in context: A295542 A089917 A294388 * A187646 A347482 A170948

Adjacent sequences: A281254 A281255 A281256 * A281258 A281259 A281260

Keyword

nonn,base

Author

K. D. Bajpai, Jan 18 2017

Status

approved