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A103208
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Numbers n such that 3 divides prime(1) + ... + prime(n).
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6
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10, 16, 18, 20, 24, 26, 28, 30, 32, 34, 36, 40, 42, 44, 46, 52, 54, 57, 68, 70, 74, 76, 78, 80, 82, 84, 86, 88, 90, 97, 99, 103, 105, 107, 111, 113, 119, 121, 123, 125, 127, 129, 134, 136, 138, 161, 163, 166, 169, 175, 177, 179, 185, 187, 195, 197, 199, 203, 205, 207, 211, 213
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OFFSET
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1,1
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COMMENTS
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Also, numbers n such that 3 divides the concatenation of the first n primes (see A019518).
The first comment and the description are true whenever the number of primes congruent to 1 mod 6 exceeds the number of primes congruent to 5 mod 6 and the difference is congruent to 1 mod 3 or the number of primes congruent to 5 mod 6 exceeds the number of primes congruent to 1 mod 6 and the difference is congruent to 2 mod 3. - Roderick MacPhee, Oct 30 2015
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LINKS
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MAPLE
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s1:=[2]; M:=1000; for n from 2 to M do s1:=[op(s1), s1[n-1]+ithprime(n)]; od: s1;
f:=proc(k) global M, s1; local t1, n; t1:=[]; for n from 1 to M do if s1[n] mod k = 0 then t1:=[op(t1), n]; fi; od: t1; end; f(3);
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MATHEMATICA
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f[n_] := FromDigits[ Flatten[ Table[ IntegerDigits[ Prime[i]], {i, n}]]]; Select[ Range[ 206], Mod[f[ # ], 3] == 0 &]
Flatten[Position[Accumulate[Prime[Range[250]]], _?(Divisible[#, 3]&)]] (* Harvey P. Dale, Jan 14 2016 *)
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PROG
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(PARI) a=0; b=0; for(x=3, 1000, if(prime(x)%6==1, a+=1, b+=1); if((a-b)%3==1 || (b-a)%3==2, print1(x", "))) \\ Roderick MacPhee, Oct 30 2015
(PARI) lista(nn) = { s=0; for(k=1, nn, s += prime(k); if(s % 3 == 0, print1(k, ", ")); ); } \\ Altug Alkan, Dec 04 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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