

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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



