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a(n) = ceiling(sqrt(2*A145701(n))).
2

%I #10 Mar 04 2019 06:07:52

%S 3,5,6,11,12,19,25,29,42,48,65,72,79,84,90,101,174,204,205,209,221,

%T 245,264,275,289,299,306,349,371,372,408,409,415,449,456,474,521,535,

%U 546,569,571,575,594

%N a(n) = ceiling(sqrt(2*A145701(n))).

%C If p_n is the n-th prime, then ceiling(sqrt(2p_n)) is in the sequence iff A145236(n) = A145236(n+1).

%p A145701 :=proc(n) local p; if n = 1 then return 3; end if; p := nextprime(procname(n-1)) ; while true do if isprime(p) and isprime(p+2) then if floor(sqrt(2*p)) <> floor( sqrt(2*p+4)) then return p; end if; end if; p := nextprime(p) ; end do; end proc:

%p A145714 := proc(n) ceil(sqrt(2*A145701(n))) ; end proc:

%p for n from 1 to 80 do printf("%d,\n",A145714(n)) ; end do; # _R. J. Mathar_, Aug 02 2010

%Y Cf. A145236, A145701.

%K nonn

%O 1,1

%A _Vladimir Shevelev_, Oct 16 2008

%E More terms from _R. J. Mathar_, Aug 02 2010