A389303 Averages of two successive primes (prime(k)+prime(k+1))/2 such that the ratio (prime(k+2)-prime(k+1))/(prime(k)-prime(k-1)) sets a new record.

4, 21, 111, 885, 1324, 31395, 155907, 1388481, 2238817, 2898234, 4738630, 7743228, 31354741, 35560000, 49269570, 98253519, 107580859, 122164744, 367876524, 1166781126, 1649328985, 3842610771, 13071556234, 19724087253, 27056880325, 29422942851, 50791075482, 101328529420, 148473908884

Offset

1,1

Comments

Apparently the denominator of the ratio is always 2 after the first term.

Links

Table of n, a(n) for n=1..29.

Example

a(1) = 4: 4 primes 2, 3, 5, 7; ratio (7-5)/(3-2) = 2, (3+5)/2 = 4.
a(2) = 21: 4 primes 17, 19, 23, 29; ratio (29-23)/(19-17) = 3, (19+23)/2 = 21.
a(3) = 111: 4 primes 107, 109, 113, 127; ratio (127-113)/(109-107) = 7, (109+113)/2 = 111.

Prog

(PARI) a389303(upto) = my(p1=2, p2=3, p3=5, q=0); forprime(p4=7, upto, my(r=(p4-p3)/(p2-p1)); if(r>q, print1((p2+p3)/2, ", "); q=r); p1=p2; p2=p3; p3=p4)

Crossrefs

Cf. A002822, A024675, A115401, A329160, A354604.

Sequence in context: A010908 A384830 A136786 * A301972 A026335 A027909

Adjacent sequences: A389300 A389301 A389302 * A389304 A389305 A389306

Keyword

nonn

Author

Hugo Pfoertner, Oct 06 2025

Status

approved