

A124110


Primes of the form A124080 (10 times triangular numbers) + 1.


2



11, 29, 31, 59, 61, 101, 149, 151, 211, 281, 359, 449, 659, 661, 911, 1049, 1051, 1201, 1361, 1531, 1709, 1901, 2099, 2309, 2311, 2531, 2999, 3001, 3251, 3511, 3779, 4349, 4649, 4651, 5279, 5281, 6299, 6301, 6659, 6661, 7411, 8609, 9029, 9461, 9901, 11279
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OFFSET

1,1


COMMENTS

Numbers j such that A124080(j)1 is prime or A124080(j)+1 is prime, where repetition means a twin prime, are 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 8, 9, 11, 11, 13, 14, 14, 15, 16, 17, 18, 19, 20, 21, 21, 22, 24, 24, 25, ..., .  Robert G. Wilson v, Nov 29 2006


LINKS



FORMULA

{A124080(j)1 when prime} U {A124080(j)+1 when prime} = {i = 10*T(j)1 such that i is prime} U {i = 10*T(j)+1 such that i is prime} where T(j) = A000217(j) = j*(j+1)/2.


EXAMPLE

a(1) = A124080(1)+1 = (10*T(1))  1 = 10*(1*(1+1)/2) + 1 = 10+1 = 11 is prime.
a(2) = A124080(2)1 = (10*T(2))1 = 10*(2*(2+1)/2)  1 = 301 = 29 is prime.
a(3) = A124080(2)+1 = (10*T(2))+1 = 10*(2*(2+1)/2) + 1 = 30+1 = 31 is prime.


MATHEMATICA

s = {}; Do[t = 5n(n + 1); If[PrimeQ[t  1], AppendTo[s, t  1]]; If[PrimeQ[t + 1], AppendTo[s, t + 1]], {n, 47}]; s (* Robert G. Wilson v *)


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



EXTENSIONS



STATUS

approved



