

A330883


A variation of the 'viral sequence' A334355; the same rules for a(n) apply but all numbers must be prime.


1



2, 7, 3, 5, 11, 13, 17, 31, 29, 19, 23, 41, 37, 43, 53, 61, 47, 67, 59, 73, 83, 71, 79, 89, 101, 103, 107, 97, 113, 131, 109, 127, 149, 137, 139, 151, 179, 163, 167, 157, 173, 181, 191, 193, 227, 197, 199, 211, 251, 223, 233, 239, 263, 229, 257, 269, 271, 241, 281, 277, 293, 311, 307
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OFFSET

1,1


COMMENTS

See A334355 for a description of the rules determining a(n). This sequence follows the same rules except that all terms must be prime.
Note that as the sequence starts with 2,7,3,... where 2+7+1=10 is a nonprime and 7+3+1=11 is a prime, like A334355 the terms in this sequence are therefore locked into a pattern of alternating pairs which when 1 is added form a nonprime and then a prime.


LINKS

Scott R. Shannon, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1) = 2, the smallest prime.
a(2) = 7 as a(1)+a(2) = 2+7 = 9 is a composite. Note that a(2) could not be 4 or 6 as only prime numbers are allowed, nor could it be 3 or 5 as 2+3=5 is a prime and 2+5=7 is a prime.
a(3) = 3 as a(2)+a(3) = 7+3 = 10 is a composite, and 3 is the smallest prime not yet appearing that sums with 7 to form a composite.


CROSSREFS

Cf. A334355, A000040, A002808, A001043.
Sequence in context: A326661 A326662 A011049 * A075639 A082737 A334971
Adjacent sequences: A330880 A330881 A330882 * A330884 A330885 A330886


KEYWORD

nonn


AUTHOR

Scott R. Shannon and Eric Angelini, Apr 30 2020


STATUS

approved



