

A073683


Group the primes such that the sum of each group is a prime. Each group from the second onwards should contain at least 3 primes: (2, 3), (5, 7, 11), (13, 17, 19, 23, 29), (31, 37, 41), (43, 47, 53, 59, 61), ... This is the sequence of the leading element in each group.


4



2, 5, 13, 31, 43, 67, 79, 97, 131, 179, 199, 257, 293, 313, 359, 389, 409, 431, 443, 467, 491, 509, 541, 571, 601, 991, 1163, 1523, 1549, 1607, 1627, 1723, 1747, 1787, 1831, 1873, 1907, 2039, 2243, 2269, 2287, 2333, 2347, 2389, 2459, 2521, 2543, 2557, 2593
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OFFSET

1,1


COMMENTS

First prime of nth group of successive primes in A073684.


LINKS

Table of n, a(n) for n=1..49.


EXAMPLE

Partition the sequence of primes into groups so that the sum of the terms in each group is prime: {2, 3}, {5, 7, 11}, {13, 17, 19, 23, 29}, {31, 37, 41}, {43, 47, 53, 59, 61}, {67, 71, 73}, {79, 83, 89}, {97, 101, 103, 107, 109, 113, 127}, {131, 137, 139, 149, 151, 157, 163, 167, 173}, {179, 181, 191, 193, 197},..; A073684(n) is the number of terms in nth group; A073682(n) is the sum of terms in nth group; a(n) is the first term in nth group; A077279(n) is the last term in nth group.


CROSSREFS

Cf. A073682, A073684, A073684, A077279.
Sequence in context: A065377 A215215 A077278 * A098501 A180302 A116701
Adjacent sequences: A073680 A073681 A073682 * A073684 A073685 A073686


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Aug 11 2002


EXTENSIONS

More terms from Zak Seidov, Nov 02 2002


STATUS

approved



