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A335139
a(n) = (prime(n + 1) +- k) / 2 where k is the smallest possible odd number such that a(n) is prime and a(n + 1) >= a(n).
0
2, 3, 3, 5, 7, 7, 11, 11, 13, 17, 19, 19, 23, 23, 29, 29, 31, 31, 37, 37, 41, 41, 43, 47, 53, 53, 53, 53, 59, 61, 67, 67, 71, 73, 73, 79, 83, 83, 89, 89, 89, 97, 97, 97, 101, 107, 113, 113, 113, 113, 113, 127, 127, 127, 131, 137, 137, 139, 139, 139, 149
OFFSET
1,1
COMMENTS
The sequence of k's begins {1, 1, -1, -1, 1, -3, 3, -1, -3, 3, 1, -3, 3, -1, ...}. I conjecture that the partial sums of the k's sequence change sign infinitely often and that their absolute value is less than the square root of n.
PROG
(PARI) forprime(n = 3, 300, forstep(j = 1, 999, 2, a = (n + j)/2; b =(n - j)/2; if(isprime(a), print1(a", "); break); if(isprime(b), print1(b", "); break)))
CROSSREFS
Cf. A000040.
Sequence in context: A343224 A047844 A081217 * A320036 A053271 A035360
KEYWORD
nonn
AUTHOR
Dimitris Valianatos, May 24 2020
STATUS
approved