login
A358530
a(n) = n-th prime prime(k) such that prime(k) - prime(k-1) < prime(k-1) - prime(k-2).
5
13, 19, 31, 41, 43, 61, 71, 73, 83, 101, 103, 109, 131, 139, 151, 167, 181, 193, 199, 227, 229, 241, 257, 271, 281, 283, 311, 313, 337, 349, 373, 383, 401, 421, 433, 443, 461, 463, 487, 491, 503, 523, 547, 563, 571, 593, 601, 617, 619, 641, 643, 661, 677
OFFSET
1,1
COMMENTS
This sequence, together with A358528 and A181424, partition the set of primes >= 5. The corresponding sequences of indices, A358531, A358529, and A356347, partition the set of positive integers >= 3.
FORMULA
a(n) = A151800(A051634(n)). - Andrew Howroyd, Sep 21 2024
EXAMPLE
n 1 2 3 4 5 6 7
k 6 8 11 13 14 18 20
prime(n) 13 19 31 41 43 61 71
MATHEMATICA
t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &] (* A358531 *)
Prime[t] (* A358530 *)
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 21 2022
EXTENSIONS
Incorrect formula removed by Georg Fischer, Sep 21 2024
STATUS
approved