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 A118590 Larger of two consecutive primes whose positive difference is a square. 3

%I

%S 3,11,17,23,41,47,71,83,101,107,113,131,167,197,227,233,281,311,317,

%T 353,383,401,443,461,467,491,503,617,647,677,743,761,773,827,857,863,

%U 881,887,911,941,971,1013,1091,1097,1217,1283,1301,1307,1427,1433,1451,1487

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

%C Superset of A031935 and A031505. [From _R. J. Mathar_, Aug 08 2008]

%H T. D. Noe, <a href="/A118590/b118590.txt">Table of n, a(n) for n = 1..1000</a>

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

%t Select[Table[Prime[n], {n, 2, 237}], IntegerQ[Sqrt[# - Prime[PrimePi[# - 1]]]] &] (* _Jayanta Basu_, Apr 23 2013 *)

%t 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 *)

%t Prime[#+1]&/@Flatten[Position[Differences[Prime[Range[250]]],_?(IntegerQ[ Sqrt[#]]&)]] (* _Harvey P. Dale_, May 08 2019 *)

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

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, May 07 2006

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)