A363168 Balanced primes of order 100.

27947, 111337, 193283, 197341, 197621, 347063, 809821, 955193, 1029803, 1184269, 1292971, 1609163, 1630859, 1656019, 1752449, 1883381, 1935517, 1969661, 2120221, 2156383, 2238959, 2287133, 2548631, 2592089, 2750903, 2866403, 3165769, 3257941, 3590299, 3889423

Offset

1,1

Comments

A prime p is in this sequence if the sum of the 100 consecutive primes just less than p, plus p, plus the sum of the 100 consecutive primes just greater than p, divided by 201 equals p.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..350 (all terms up to the 4 millionth prime)

Mathematica

Module[{bal=100, nn=300000}, Select[Partition[Prime[Range[nn]], 2bal+1, 1], Mean[#]== #[[bal+1]]&]] [[;; , 101]]

Crossrefs

Cf. Balanced primes of order b: A006562 (b=1), A082077 (b=2), A082078 (b=3), A082079 (b=4), A096697 (b=5), A096698 (b=6), A096699 (b=7), A096700 (b=8), A096701 (b=9), A096702 (b=10), A096703 (b=11), A096704 (b=12), A300364 (b=13), A300365 (b=14).

Sequence in context: A046333 A202403 A206618 * A233430 A220986 A242607

Adjacent sequences: A363165 A363166 A363167 * A363169 A363170 A363171

Keyword

nonn

Author

Harvey P. Dale, Jul 07 2023

Status

approved