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
Keywords
Examples
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.
Links
- Ruud H.G. van Tol, Table of n, a(n) for n = 1..80
Programs
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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]);
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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
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