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A172112 Partial sums of A023200. 1
3, 10, 23, 42, 79, 122, 189, 268, 365, 468, 577, 704, 867, 1060, 1283, 1512, 1789, 2096, 2409, 2758, 3137, 3534, 3973, 4430, 4893, 5380, 5879, 6492, 7135, 7808, 8547, 9304, 10073, 10896, 11749, 12608, 13485, 14368, 15275, 16212, 17179, 18188, 19275 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes in the partial sum begin: a(1) = 3, a(3) = 23, a(5) = 79, a(11) = 577, a(15) = 1283, a(17) = 1789, a(21) = 3137, a(27) = 5879. Of these, the smaller members of cousin prime pairs which appear among the partial sums of smaller member p of cousin prime pairs begin: 3, 79; which are the next in this subset?

LINKS

Table of n, a(n) for n=1..43.

FORMULA

a(n) = SUM[i=i..n] A023200(i) = SUM[i=i..n] {Primes p such that p and p + 4 are both primes}.

EXAMPLE

a(30) = 3 + 7 + 13 + 19 + 37 + 43 + 67 + 79 + 97 + 103 + 109 + 127 + 163 + 193 + 223 + 229 + 277 + 307 + 313 + 349 + 379 + 397 + 439 + 457 + 463 + 487 + 499 + 613 + 643 + 673 = 7808.

CROSSREFS

Cf. A000040, A023200, A046132.

Sequence in context: A041403 A077126 A172113 * A227347 A068043 A145069

Adjacent sequences:  A172109 A172110 A172111 * A172113 A172114 A172115

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Jan 25 2010

EXTENSIONS

More terms from Max Alekseyev, Jan 31 2010

STATUS

approved

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Last modified August 29 08:06 EDT 2015. Contains 261188 sequences.