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.
A242478
Primes p such that, in base 17, p = the cumulative sum of the digit-mult(digit-sum(prime)) of each prime < p.
Original entry on oeis.org
5, 57839, 58013, 105683, 160367, 926899, 926983, 927007, 928819, 963121, 963223, 2329777, 2384821, 2384881, 3228713, 3228751, 3229081, 3229097, 3246653, 3259547, 7327781, 7339447
Offset: 1
5 = digit-mult(digit-sum(2)) + digit-mult(digit-sum(3)). 57839 = digit-mult(digit-sum(2)) + digit-mult(digit-sum(3)) + ... digit-mult(digit-sum(BD1C)) = digit-mult(2) + digit-mult(3) + ... digit-mult(23) = 2 + 3 + ... 2*3. Note that BD1C and 23 in base 17 = 57829 and 37 in base 10.
A242479
Primes p such that, in base 17, p = the cumulative sum of the digit-mult(digit-sum(prime)) of each prime <= p.
Original entry on oeis.org
105701, 160309, 927137, 927149, 964973, 2329081, 2329097, 2329549, 2384587, 3228733, 3237527, 3242851, 7338377, 7338431, 7338557, 7338719
Offset: 1
105701 = digit-mult(digit-sum(2)) + digit-mult(digit-sum(3)) + ... digit-mult(digit-sum(148CC)) = digit-mult(2) + digit-mult(3) + ... digit-mult(23) = 2 + 3 + ... 2*3. Note that 148CC and 23 in base 17 = 105701 and 37 in base 10.
A242589
Primes p such that p = the cumulative sum of the digit-sum in base 15 of the digit-product in base 4 of each prime < p.
Original entry on oeis.org
5, 19, 37, 43, 97, 107, 6091, 6389, 7121, 21727, 147107, 148151, 148279, 148429, 148469, 172877, 173209, 173741, 2621387, 5642293, 5642321, 8932771, 8981827, 8981879, 9094979, 9095089, 9997783, 10010687, 10010789, 10037749, 10144523, 40179929, 40365217, 40379077, 40379197, 40386811, 40612933
Offset: 1
5 = digit-sum(digit-mult(2,b=4),b=15) + sum(mult(3,b=4),b=15) = 2 + 3.
19 = digit-sum(digit-mult(2,b=4),b=15) + sum(mult(3,b=4),b=15) + sum(mult(11,b=4),b=15) + sum(mult(13,b=4),b=15) + sum(mult(23,b=4),b=15) + sum(mult(31,b=4),b=15) + sum(mult(101,b=4),b=15) = 2 + 3 + 1 + 3 + 6 + 3 + 1.
Cf.
A240886 (similar sequence with digit sums in base 3).
Showing 1-6 of 6 results.
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