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

Author

Massimo Kofler, Oct 08 2023

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A000040, A013929.

Intersection of A023200 and A061400.

Cf. A061368.

Programs

Mathematica

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

PARI

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