1,2

Define b(0)=2, b(1)=5 and b(n)=6*b(n-1)-b(n-2)-2 for n>1. A prime number p is in the sequence iff (p^2-p-2)/2 is a square iff p=b(n) for some n. The next prime in the sequence is b(21)=8946229758127349, followed by b(n) for n=33, 51, 57 and 75.

a(18) > 3*10^9. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 14 2009]

s(n)=A000217[n]-A000203[n]=A024816[n] is a square.

The sum of the non-divisors of 14 between 1 and 14 is 3 + 4 + 5 + 6 + 8 + 9 + 10 + 11 + 12 + 13 = 81 = 9^2. 1, 2, 7 & 14 are divisors. Hence 14 is a term of the sequence.

Select[ Range[14*10^6], IntegerQ[Sqrt[(# (# + 1)/2) - DivisorSigma[1, # ]]] &]

Sequence in context: A100630 A057302 A109784 this_sequence A050216 A037079 A101325

Adjacent sequences: A076621 A076622 A076623 this_sequence A076625 A076626 A076627

nonn

Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Oct 22 2002

Edited by Robert G. Wilson v (rgwv(AT)rgwv.com) and Dean Hickerson (dean.hickerson(AT)yahoo.com), Oct 25 2002

a(16)-a(17) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Oct 14 2009