A281257 - OEIS

%I #22 Jan 20 2017 13:52:05

%S 11,223,2556997,3333331,14559007,47836783,56672227,65555671,181114559,

%T 411488881,583227779,1399999987,5723503439,10047846871,11361255547,

%U 13787777879,18474111311,19905449987,20235780199,21226777753,22557892319,71445725647,83447001413,103459003423

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

%C Intersection of A000040 and A067894.

%H Robert Israel, <a href="/A281257/b281257.txt">Table of n, a(n) for n = 1..10000</a>

%e 0 + 1 + 10 = 11 (prime), so 11 is in the sequence.

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

%p select(isprime, ListTools:-PartialSums(map(convert,[$1..1000],binary))); # _Robert Israel_, Jan 18 2017

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

%o (PARI) F(k,{b=10})=sum(i=1,k,subst(Pol(binary(i),y),y,b));

%o test(k,{b=10})={my(z=F(k,b));return(isprime(z)*z)};

%o 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]))}

%o 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

%Y Cf. A000040, A007088, A067894.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Jan 18 2017