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%I #4 Jun 09 2015 12:00:12
%S 10007,20016,60025,130026,200029,270038,360039,450046,550049,750052,
%T 950061,1250068,1650077,2150086,2850087,3750088,4650095,5650098,
%U 6650131,7650168,8650207,9650288,10650387,11650690,12651093,13651502,14652009,15652618,16653525
%N Partial sums of naughty primes A164968.
%C The subsequence of prime partial sums of naughty primes begins: 10007, 200029, 550049, 6650131. The subsubsequence of naughty prime partial sums of naughty primes begins: 10007, and then what? The smallest square in the sequence is 60025 = 5^2 * 7^4.
%F a(n) = SUM[i=1..n] {p such that p is prime and the number of zeros in the decimal representation of p is greater than the number of all other digits}.
%e a(24) = 10007 + 10009 + 40009 + 70001 + 70003 + 70009 + 90001 + 90007 + 100003 + 200003 + 200009 + 300007 + 400009 + 500009 + 700001 + 900001 + 900007 + 1000003 + 1000033 + 1000037 + 1000039 + 1000081 + 1000099 + 1000303.
%t Accumulate[Select[Prime[Range[100000]],DigitCount[#,10,0]> IntegerLength[ #]/2&]] (* _Harvey P. Dale_, Jun 09 2015 *)
%Y Cf. A000040, A164968.
%K base,easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 07 2010
%E Corrected and extended by _Harvey P. Dale_, Jun 09 2015