A106155 Numbers k > 2 such that prime(k)# + (prime(k+1))^2 or prime(k+1)# - (prime(k+2))^2 is prime or both are primes.
3, 4, 5, 6, 7, 10, 12, 13, 19, 26, 28, 41, 66, 73, 76, 78, 85, 371, 437, 513, 661, 726, 924, 1063, 1331, 1380, 1422, 1602, 1947, 1963, 3091, 3295, 3401
Offset: 1
Examples
2*3*5 + 7*7 = 79 prime as 2*3*5*7 - 11*11 = 89 prime so a(1)=3. 2*3*5*7 + 11*11 = 331 prime as 2*3*5*7*11 -13*13 = 2141 prime so a(2)=4. 2*3*5*7*11 + 13*13 = 2479 = 37*67 composite. 2*3*5*7*11*13 - 17*17 = 29471 prime so a(3)=5.
Extensions
a(20)-a(30) from Donovan Johnson, Apr 27 2008
a(31)-a(33) from Michael S. Branicky, Jun 09 2023