A364778 Products of two distinct strong primes.

121, 187, 289, 319, 407, 451, 493, 629, 649, 697, 737, 781, 841, 869, 1003, 1067, 1073, 1111, 1139, 1177, 1189, 1207, 1343, 1369, 1397, 1507, 1517, 1639, 1649, 1681, 1711, 1717, 1793, 1819, 1943, 1969, 2059, 2101, 2159, 2167, 2183, 2291, 2329, 2419, 2453, 2479, 2497, 2533, 2627, 2629, 2747

Offset

1,1

Comments

Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.

Links

Table of n, a(n) for n=1..51.

Example

121 = 11^2 and 11 > (7+13)/2.
187 = 11*17 and 11 > (7+13)/2, 17 > (13+19)/2.
493 = 17*29 and 17 > (13+19)/2, 29 > (23+31)/2.

Mathematica

strongQ[p_] := p > 2 && 2*p > Total[NextPrime[p, {-1, 1}]]; Select[Range[1, 3000, 2], MemberQ[{{1, 1}, {2}}, (f = FactorInteger[#])[[;; , 2]]] && AllTrue[f[[;; , 1]], strongQ] &] (* Amiram Eldar, Aug 07 2023 *)

Crossrefs

Cf. A001358, A051634, A363167, A363782.

Sequence in context: A284643 A074730 A268519 * A037050 A275028 A036309

Adjacent sequences: A364775 A364776 A364777 * A364779 A364780 A364781

Keyword

nonn

Author

Massimo Kofler, Aug 07 2023

Extensions

Definition clarified by N. J. A. Sloane, Oct 08 2023

Status

approved