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A103208 Numbers n such that 3 divides prime(1) + ... + prime(n). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Hisanori Mishima, Smarandache consecutive prime sequences (n = 1 to 100).

MAPLE

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);

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A007504, A019518, A104644, A111287.

Sequence in context: A109891 A104869 A104868 * A323196 A187797 A192221

Adjacent sequences:  A103205 A103206 A103207 * A103209 A103210 A103211

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Mar 19 2005

EXTENSIONS

Entry revised by N. J. A. Sloane, Nov 09 2005

STATUS

approved

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Last modified May 22 15:13 EDT 2019. Contains 323480 sequences. (Running on oeis4.)