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

Author

Harvey P. Dale, Jul 07 2023

Keywords

• nonn

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)

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).

Programs

Mathematica

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