A366352 Lesser of 2 successive primes (k, k+4) sandwiching 3 consecutive nonsquarefree numbers.

97, 349, 1447, 1663, 2347, 3697, 9547, 13147, 13309, 13687, 14533, 14947, 15727, 16603, 21139, 24547, 24847, 26557, 27733, 31147, 32797, 33613, 34603, 35593, 36943, 38149, 38707, 40849, 41047, 42433, 44449, 44647, 45763, 45949, 46447, 50047, 52387, 58147, 58309

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Example

97 and 101 are prime numbers; 98 = 2 * 7^2, 99 = 3^2 * 11 and 100 = 2^2 * 5^2 are 3 consecutive nonsquarefree numbers, so 97 is a term.
349 and 353 are prime numbers; 350 = 2 * 5^2 * 7, 351 = 3^3 * 13, 352 = 2^5 * 11 are 3 consecutive nonsquarefree numbers, so 349 is a term.

Mathematica

Select[Partition[Prime[Range[6000]], 2, 1], Differences[#] == {4} && AllTrue[Range[First[#] + 1, Last[#] - 1], ! SquareFreeQ[#1] &] &][[;; , 1]] (* Amiram Eldar, Oct 08 2023 *)

Prog

(PARI) isok(p) = isprime(p) && (nextprime(p+1) - p == 4) && (sum(k=1, 3, issquarefree(p+k)) == 0); \\ Michel Marcus, Oct 08 2023

Crossrefs

Cf. A000040, A013929.

Intersection of A023200 and A061400.

Cf. A061368.

Sequence in context: A142631 A087861 A269786 * A105128 A031927 A174338

Adjacent sequences: A366349 A366350 A366351 * A366353 A366354 A366355

Keyword

nonn

Author

Massimo Kofler, Oct 08 2023

Status

approved