

A235681


Primes p with prime(p)  p + 1 and p*(p+1)  prime(p) both prime.


4



2, 3, 5, 41, 61, 71, 89, 271, 281, 293, 337, 499, 571, 751, 907, 911, 1093, 1531, 2027, 2341, 2707, 2861, 3011, 3359, 3391, 3511, 4133, 5179, 5189, 5483, 5573, 5657, 5867, 6577, 6827, 7159, 7411, 7753, 7879, 8179, 8467, 9209, 9391, 9419, 9433, 10259, 10303, 10859, 10993, 11287
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

This is the intersection of A234695 and A235661. For any prime p in this sequence, p^2 + 1 is the sum of the two primes prime(p)  p + 1 and p*(p+1)  prime(p).
By the conjecture in A235682, this sequence should have infinitely many terms.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1) = 2 since prime(2)  2 + 1 = 2 and 2*3  prime(2) = 3 are both prime.
a(2) = 3 since prime(3)  3 + 1 = 3 and 3*4  prime(3) = 7 are both prime.
a(3) = 5 since prime(5)  5 + 1 = 7 and 5*6  prime(5) = 19 are both prime.


MATHEMATICA

PQ[n_]:=PrimeQ[Prime[n]n+1]&&PrimeQ[n(n+1)Prime[n]]
n=0; Do[If[PQ[Prime[k]], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 1000}]


CROSSREFS

Cf. A000040, A234694, A234695, A232353, A235189, A235330, A235613, A235614, A235661, A235682.
Sequence in context: A215309 A215105 A088483 * A322748 A224781 A136015
Adjacent sequences: A235678 A235679 A235680 * A235682 A235683 A235684


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Jan 13 2014


STATUS

approved



