A354284 The first of four consecutive primes p1, p2, p3, p4 such that (p4-p3)*(p2-p1) = (p3-p2)^2.

89, 251, 449, 1061, 1439, 1741, 1997, 2237, 2239, 2267, 2593, 2657, 2699, 3301, 3433, 3449, 5101, 5189, 5237, 5381, 6197, 6311, 6361, 6599, 6827, 6829, 6883, 7433, 8087, 8171, 8311, 9067, 10259, 12149, 12611, 12641, 13451, 14741, 15791, 15901, 16787, 17027, 17291, 17387, 17389, 17471, 18211

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 449 is a term because the four consecutive primes starting with 449 are 449, 457, 461, 463, and (463-461)*(457-449) = (461-457)^2 = 16.

Maple

P:= select(isprime, [seq(i, i=3..20000, 2)]):
R:= select(t -> (P[t+3]-P[t+2])*(P[t+1]-P[t]) = (P[t+2]-P[t+1])^2, [$1..nops(P)-3]):
P[R];

Mathematica

Select[Partition[Prime[Range[2000]], 4, 1], (#[[4]] - #[[3]])*(#[[2]] - #[[1]]) == (#[[3]] - #[[2]])^2 &][[;; , 1]] (* Amiram Eldar, May 23 2022 *)

Prog

(Python)
from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
    p1, p2, p3, p4 = 2, 3, 5, 7
    while True:
        if (p4-p3)*(p2-p1) == (p3-p2)**2: yield p1
        p1, p2, p3, p4 = p2, p3, p4, nextprime(p4)
print(list(islice(agen(), 47))) # Michael S. Branicky, May 22 2022

Crossrefs

Sequence in context: A248745 A033257 A145821 * A142655 A140040 A008900

Adjacent sequences: A354281 A354282 A354283 * A354285 A354286 A354287

Keyword

nonn

Author

J. M. Bergot and Robert Israel, May 22 2022

Status

approved