A069496 - OEIS

%I #39 Jan 05 2020 08:31:18

%S 17,71,881,1151,2591,3527,4049,15137,20807,34847,46817,69191,83231,

%T 103967,112337,149057,176417,179999,206081,281249,362951,388961,

%U 438047,472391,478241,538721,649799,734471,808991,960497,1080449,1143071

%N Smaller member of a twin prime pair with a square sum.

%C All members of this sequence have digital root 8. - _J. W. Helkenberg_, Jul 24 2013

%C First bisection of A232878. - _Gary Croft_, Dec 05 2013

%H T. D. Noe, <a href="/A069496/b069496.txt">Table of n, a(n) for n = 1..10000</a>

%H Author?, <a href="http://www.kfki.hu/chemonet/TermVil/tv2002/tv0204/tartalom.html">Title?</a> (no longer exists)

%F a(n) = (A037072(n)-2)/2.

%F a(n) = A118593(n) - 2. - _Zerinvary Lajos_, Jul 31 2006

%e 71 is a term as the smaller member of the twin prime pair (71,73) as 71+73 = 144 = 12^2.

%p isa := n -> isprime(n) and isprime(n+2) and issqr(2*n+2):

%p select(isa, [$4..1000000]); # _Peter Luschny_, Jan 05 2020

%t First/@Select[Partition[Prime[Range[9*10^4]],2,1],Differences[#]=={2} && IntegerQ[Sqrt[Total[#]]] &] (* _Jayanta Basu_, May 26 2013 *)

%o (PARI) t(n, p=3) = {while( p+2 < (p=nextprime( p+1 )) || n-->0, ); p-2}

%o for(n=1, 1e4, if(issquare(2*t(n)+2), print1(t(n), ", "))); \\ _Altug Alkan_, Mar 14 2016

%Y Cf. A118593, A232878.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Mar 30 2002

%E More terms from _Sascha Kurz_, Apr 01 2002