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A348176
Numbers m such that the number of symmetrically distributed consecutive primes centered at m sets a new record.
0
1, 2, 4, 5, 9, 12, 30, 165, 8021811, 1071065190, 1613902650, 1797595815015, 633925574060895
OFFSET
1,2
COMMENTS
Conjecture: This sequence is infinite.
EXAMPLE
n a(n) = m A346399(m) Symmetrical consecutive primes centered at m
-- ---------- ---------- --------------------------------------------
1 1 0 { }
2 2 1 {2}
3 4 2 {3,5}
4 5 3 {3,5,7}
5 9 4 {5,7,11,13}
6 12 6 {5,7,11,13,17,19}
7 30 10 {13,17,19,23,29,31,37,41,43,47}
8 165 12 {m +- 2,8,14,16,26,28}
9 8021811 14 {m +- 10,20,22,40,52,58,62}
10 1071065190 16 {m +- 11,23,37,49,53,61,67,79}
11 1613902650 18 {m +- 1,7,23,29,49,77,83,89,97}
PROG
(Python)
from sympy import isprime
rec = -1
for n in range(1, 10**10):
d = 1 if n%2 == 0 else 2
ct = 1 if isprime(n) else 0
while n - d > 2:
k = isprime(n+d) + isprime(n-d)
if k == 2: ct += 2
elif k == 1: break
d += 2
if ct > rec: print(n, end = ', '); rec = ct
CROSSREFS
Cf. A346399.
Sequence in context: A240576 A060312 A218934 * A325716 A068372 A068370
KEYWORD
nonn,more
AUTHOR
Ya-Ping Lu, Oct 05 2021
EXTENSIONS
a(12)-a(13) from Martin Ehrenstein, Nov 21 2021
STATUS
approved