A118590 Larger of two consecutive primes whose positive difference is a square.

3, 11, 17, 23, 41, 47, 71, 83, 101, 107, 113, 131, 167, 197, 227, 233, 281, 311, 317, 353, 383, 401, 443, 461, 467, 491, 503, 617, 647, 677, 743, 761, 773, 827, 857, 863, 881, 887, 911, 941, 971, 1013, 1091, 1097, 1217, 1283, 1301, 1307, 1427, 1433, 1451, 1487

Offset: 1

Author

Cino Hilliard, May 07 2006

Keywords

• easy
• nonn

Examples

			7 and 11 are consecutive primes. 11-7 = 4 a square, so 11 is the second term in the table.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Index entries for primes, gaps between

Crossrefs

Cf. A031935, A031505, A134117 (gap 6^2), A204670 (gap 8^2), A050434 (gap 10^2), A138198, A161002.

Programs

Mathematica

Select[Table[Prime[n], {n, 2, 237}], IntegerQ[Sqrt[# - Prime[PrimePi[# - 1]]]] &] (* Jayanta Basu, Apr 23 2013 *)
nn = 500; ps = Prime[Range[nn]]; t = {}; Do[If[IntegerQ[Sqrt[ps[[n]] - ps[[n-1]]]], AppendTo[t, ps[[n]]]], {n, 2, nn}]; t (* T. D. Noe, Apr 23 2013 *)
Prime[#+1]&/@Flatten[Position[Differences[Prime[Range[250]]],?(IntegerQ[ Sqrt[#]]&)]] (* _Harvey P. Dale, May 08 2019 *)

PARI

g(n) = for(x=2, n, if(issquare(prime(x)-prime(x-1)), print1(prime(x)",")))

Formula

Superset of A031935 and A031505. [From R. J. Mathar, Aug 08 2008]