

A118590


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


3



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
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OFFSET

1,1


COMMENTS

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


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


EXAMPLE

7 and 11 are consecutive primes. 117 = 4 a square, so 11 is the second term in the table.


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[[n1]]]], 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 *)


PROG

(PARI) g(n) = for(x=2, n, if(issquare(prime(x)prime(x1)), print1(prime(x)", ")))


CROSSREFS

Sequence in context: A108328 A153419 A079020 * A136082 A106083 A113803
Adjacent sequences: A118587 A118588 A118589 * A118591 A118592 A118593


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, May 07 2006


STATUS

approved



