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A138042 Numbers k such that A096379(k)=A096379(k+1).

%I A138042 #11 Jul 09 2025 23:32:32
%S A138042 2,7,13,19,49,69,116,182,206,225,229,236,253,265,288,315,324,352,379,
%T A138042 390,394,435,492,497,542,551,567,625,643,658,718,754,794,920,930,935,
%U A138042 958,966,988,1025,1032,1085,1101,1128,1155,1171,1173,1225,1235,1249
%N A138042 Numbers k such that A096379(k)=A096379(k+1).
%C A138042 Numbers k such that prime(k)=2*prime(k+2)-prime(k+3).
%H A138042 Zak Seidov, <a href="/A138042/b138042.txt">Table of n, a(n) for n = 1..1192, a(n)<50000.</a>
%F A138042 a(n) = A066495(n) - 2.
%e A138042 n=2: {prime(n), 2*prime(n+2)-prime(n+3)}={3,2*7-11},
%e A138042 n=7: {prime(7), 2*prime(9)-prime(10)}={17,2*23-29},
%e A138042 n=13: {prime(13), 2*prime(15)-prime(16)}={41,2*47-53},
%e A138042 n=19: {prime(19), 2*prime(21)-prime(22)}={67,2*73-79}.
%t A138042 Do[If[Prime[n]==2Prime[n+2]-Prime[n+3],Print[n]],{n,1,50000}]
%o A138042 (Scheme)
%o A138042 ;; With _Antti Karttunen_'s IntSeq-library.
%o A138042 (define A138042 (MATCHING-POS 1 1 (lambda (n) (= 2 (/ (+ (A000040 n) (A000040 (+ n 3))) (A000040 (+ n 2)))))))
%Y A138042 Cf. A066495, A096379.
%K A138042 nonn
%O A138042 1,1
%A A138042 _Zak Seidov_, Mar 02 2008
%E A138042 Formula corrected by _Antti Karttunen_, Jul 13 2013