A168162
Numbers n which do not exceed the sum of the binary digits in all primes <= n.
Original entry on oeis.org
3, 5, 7, 8, 11, 13, 14, 19, 23, 31, 32, 47, 61
Offset: 1
There is no prime <= 1 and 2 has only nonzero binary digit, therefore these numbers are not in the sequence.
However, a(1)=3 has two binary digits, so the total number of these equal 3.
Then, 4 is larger than this, but the prime p=5 again adds 2 nonzero binary digits adding to a total of 5=a(2).
Then 6 is larger than this, but the prime p=7 adds 3 more nonzero bits for a total of 8, such that a(3)=7 and a(4)=8 don't exceed this.
A217792
Primes which are equal to the sum of the binary digits of consecutive primes starting with 2.
Original entry on oeis.org
3, 5, 11, 19, 23, 47, 61, 71, 101, 127, 131, 179, 211, 223, 293, 347, 383, 397, 401, 419, 433, 491, 547, 563, 577, 587, 641, 647, 683, 757, 859, 929, 947, 1019, 1093, 1123, 1181, 1187, 1303, 1319, 1327, 1381, 1409, 1543, 1831, 1847, 1877, 1997, 2003, 2113
Offset: 1
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Select[Accumulate[Total/@IntegerDigits[Prime[Range[1000]],2]],PrimeQ]
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t=0;forprime(p=2,1e4,if(isprime(t+=hammingweight(p)),print1(t", "))) \\ Charles R Greathouse IV, Mar 25 2013
A241897
Primes p equal to the sum in base 3 of the digits of all primes < p - digit-sum of the index of prime p(i-1).
Original entry on oeis.org
67, 71, 97, 101, 149, 223, 656267, 697511, 697951, 698447, 699493, 700277, 715373, 883963, 888203, 888211, 992021, 992183, 992891, 993241, 994181, 1155607, 1155829, 1308121, 1308649, 1310093, 1313083, 1317409, 1320061, 1320157, 1320379, 1322521, 1322591
Offset: 1
67 = digit-sum(2..61,b=3) - digit-sum(index(61),b=3) = sum(2) + sum(1,0) + sum(1,2) + sum(2,1) + sum(1,0,2) + sum(1,1,1) + sum(1,2,2) + sum(2,0,1) + sum(2,1,2) + sum(1,0,0,2) + sum(1,0,1,1) + sum(1,1,0,1) + sum(1,1,1,2) + sum(1,1,2,1) + sum(1,2,0,2) + sum(1,2,2,2) + sum(2,0,1,2) + sum(2,0,2,1) - digit-sum(200).
A240886. Primes p equal to the digit-sum in base 3 of all primes < p.
A168161. Primes p which are equal to the sum of the binary digits in all primes <= p.
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seq(maxp)={my(p=1,L=List(),s=0,k=0); while(pAndrew Howroyd, Mar 01 2018
A241895
Primes p equal to the sum in base 3 of the digits of all primes <= p.
Original entry on oeis.org
3, 37, 695663, 695881, 1308731, 1308757, 1313153, 1314301, 1326097, 1766227, 3204779, 14328191
Offset: 1
3 = digit-sum(primes <= 3,base=3) = sum(2) + sum(1,0). 37 = digit-sum(primes <= 37,base=3) = sum(2) + sum(1,0) + sum(1,2) + sum(2,1) + sum(1,0,2) + sum(1,1,1) + sum(1,2,2) + sum(2,0,1) + sum(2,1,2) + sum(1,0,0,2) + sum(1,0,1,1) + sum(1,1,0,1).
Cf.
A168161 (similar in base 2),
A240886 (similar but excluding p from the sum).
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sdt(n) = my(d = digits(n, 3)); sum(i=1, #d, d[i]);
lista(nn) = {sp = 0; forprime(p=1, nn, sp += sdt(p); if (p == sp, print1(p, ", ")););} \\ Michel Marcus, May 02 2014
A241896
Increasingly ordered odd primes p(m) with p(m) = (sum of the digits of all primes p(i) in base 3 for i=1, 2, ..., m-1) + (sum of digits of m-1 in base 3).
Original entry on oeis.org
3, 5, 7, 11, 17, 29, 37, 695641, 695687, 695749, 695881, 699943, 700199, 715457, 883433, 883451, 883471, 883621, 992111, 992357, 992591, 993683, 1308563, 1309999, 1310041, 1310359, 1310993, 1313161, 1314191, 1314377, 1317271, 1324567, 1326097, 1326109, 1326649, 1760113, 1760287, 1766509, 1766537, 3173761, 3204779, 3204827, 4539191
Offset: 1
prime(2) = 3 = A239619(1) + A053735(1) = 2 + 1. This is a(1) because it is the smallest odd prime from the defined set S.
prime(7) = 17 = sum_{i=1..6} A239619(i) + A053735(6) = (2 + 1 + 3 + 3 + 3 + 3) + 2 = 17. This is a(5) because it is the fifth smallest odd prime from the set S.
prime(6) = 13 is not a member of this sequence because (2 + 1 + 3 + 3 + 3) + 3 = 15 which is not equal 13, hence prime(6) is not a member of the set S.
Showing 1-5 of 5 results.
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