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A281257 Primes in A067894: primes in the partial sums of the binary representations of the first m natural numbers, reading these representations in decimal. 1
11, 223, 2556997, 3333331, 14559007, 47836783, 56672227, 65555671, 181114559, 411488881, 583227779, 1399999987, 5723503439, 10047846871, 11361255547, 13787777879, 18474111311, 19905449987, 20235780199, 21226777753, 22557892319, 71445725647, 83447001413, 103459003423 (list; graph; refs; listen; history; text; internal format)
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 A170948 A245076

Adjacent sequences:  A281254 A281255 A281256 * A281258 A281259 A281260

KEYWORD

nonn,base

AUTHOR

K. D. Bajpai, Jan 18 2017

STATUS

approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)