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Primes which are equal to the sum of the binary digits of consecutive primes starting with 2.
2

%I #16 May 13 2013 01:54:22

%S 3,5,11,19,23,47,61,71,101,127,131,179,211,223,293,347,383,397,401,

%T 419,433,491,547,563,577,587,641,647,683,757,859,929,947,1019,1093,

%U 1123,1181,1187,1303,1319,1327,1381,1409,1543,1831,1847,1877,1997,2003,2113

%N Primes which are equal to the sum of the binary digits of consecutive primes starting with 2.

%C This is similar to A168161 except for eliminating the requirement that the primes whose binary digits are summed be less than or equal to the resulting (sum-of-binary-digits) prime.

%H Charles R Greathouse IV, <a href="/A217792/b217792.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Accumulate[Total/@IntegerDigits[Prime[Range[1000]],2]],PrimeQ]

%o (PARI) t=0;forprime(p=2,1e4,if(isprime(t+=hammingweight(p)),print1(t", "))) \\ _Charles R Greathouse IV_, Mar 25 2013

%Y Cf. A168161.

%K nonn,base

%O 1,1

%A _Harvey P. Dale_, Mar 25 2013