A181994 Initial members of prime triples p < q < r such that r-q = n*(q-p).

3, 2, 29, 8117, 137, 197, 45433, 1931, 521, 156151, 1949, 1667, 480203, 2969, 7757, 2181731, 12161, 28349, 6012893, 20807, 16139, 3933593, 163061, 86627, 13626251, 25469, 40637, 60487753, 79697, 149627, 217795241, 625697, 552401, 240485251, 173357, 360089, 122164741

Offset: 1

Author

Zak Seidov, May 31 2012

Keywords

• nonn

Comments

For some n, a(n) are abnormally large: note, e.g., that if q-p=2, then n cannot be of the form 4+3k, that is why a(4), a(7), a(10), ... are larger than neighbor terms; also, a(67) > 1.1*10^11. Is the sequence infinite?

Examples

			First 10 cases of {n,p,q,r}: {1,3,5,7}, {2,2,3,5}, {3,29,31,37}, {4,8117,8123,8147}, {5,137,139,149}, {6,197,199,211}, {7,45433,45439,45481}, {8,1931,1933,1949}, {9,521,523,541}, {10,156151,156157,156217}.
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..66

Crossrefs

Particular cases with q-p=2: A022004 [(r-q)=2*(q-p)], A049437 [(r-q)=3*(q-p) starting with 2nd term].

Cf. A179210.

Formula

a(n) = prevprime(A179210(n)). - Robert G. Wilson v, Dec 23 2016