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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
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
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 = 30-1 = 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 *)
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Nov 26 2006
EXTENSIONS
More terms from Robert G. Wilson v, Nov 29 2006
STATUS
approved