A374576 a(n) is the smallest prime prime(k) such that prime(k-n) and prime(k+n) are balanced primes of order n.

7829, 18713, 211, 19891, 2381, 63649, 183971, 11287, 67957, 2197697, 345749, 1359913, 2267827, 543383, 16705691, 2667311, 3369869, 38094029, 35605289, 3303059, 26184253, 44116757, 4271017, 35099179, 44191919, 296115661, 86828801, 169863823, 991, 163355419, 10301623, 115044443, 240284293

Offset

1,1

Comments

a(n) is the least prime that is the start and end of sequences of 2*n+1 consecutive primes whose arithmetic means are their medians.

Links

Ruud H.G. van Tol, Table of n, a(n) for n = 1..80

Example

a(3) = 211 because the 7 consecutive primes 179, 181, 191, 193, 197, 199, 211 ending at 211 have mean = median = 193 and the 7 consecutive primes 211, 223, 227, 229, 233, 239, 241 starting at 211 have mean = median = 229, and 211 is the first prime for which this works.

Maple

f:= proc(n)
 local S, i;
 S:= [seq](ithprime(i), i=1..4*n+1);
 do
   if convert(S[1..2*n+1], `+`) = (2*n+1)*S[n+1] and convert(S[2*n+1..4*n+1], `+`) = (2*n+1)*S[3*n+1] then
   return S[2*n+1] fi;
   S:= [op(S[2..-1]), nextprime(S[-1])]
 od;
end proc:
map(f, [$1..35]);

Prog

(PARI) alist(N) = {my(r=vector(N), p=primes(4*N+1), t); while(t=Vec(select(x->!x, r, 1)), foreach(t, n, my(w=2*n+1); if(vecsum(p[1..w])==w*p[1+n] && vecsum(p[w..2*w-1])==w*p[w+n], r[n]=p[w])); p=primes([p[2], nextprime(p[#p]+1)])); r; } \\ Ruud H.G. van Tol, Jul 13 2024

Crossrefs

Cf. A082080, A374507.

Sequence in context: A375916 A252317 A250026 * A374507 A194352 A234477

Adjacent sequences: A374573 A374574 A374575 * A374577 A374578 A374579

Keyword

nonn

Author

Robert Israel, Jul 11 2024

Status

approved