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A066495 Numbers k such that f(k) = f(k-1) + f(k-2) where f denotes the prime gaps function given by f(m) = prime(m+1) - prime(m).

%I A066495 #21 Aug 14 2023 02:00:38
%S A066495 4,9,15,21,51,71,118,184,208,227,231,238,255,267,290,317,326,354,381,
%T A066495 392,396,437,494,499,544,553,569,627,645,660,720,756,796,922,932,937,
%U A066495 960,968,990,1027,1034,1087,1103,1130,1157,1173,1175,1227,1237,1251
%N A066495 Numbers k such that f(k) = f(k-1) + f(k-2) where f denotes the prime gaps function given by f(m) = prime(m+1) - prime(m).
%H A066495 Robert Israel, <a href="/A066495/b066495.txt">Table of n, a(n) for n = 1..10000</a>
%F A066495 a(n) = A138042(n) + 2 [based on the formula found from A138042]. - _Antti Karttunen_, Jul 13 2013
%e A066495 f(9) = 6 = 4 + 2 = f(8) + f(7); so 9 is a term.
%t A066495 f[n_] := Prime[n + 1] - Prime[n]; Select[Range[3, 10^4], f[ # ] == f[ # - 1] + f[ # - 2] &]
%o A066495 (Scheme with _Antti Karttunen_'s IntSeq-library)
%o A066495 (define A066495 (MATCHING-POS 1 1 (lambda (n) (and (> n 2) (= (A001223 n) (+ (A001223 (- n 1)) (A001223 (- n 2))))))))
%o A066495 (define (A066495v2 n) (+ 2 (A138042 n))) ;; Alternative definition.
%Y A066495 Cf. A000040 (function p in the definition).
%Y A066495 Cf. A001223 (function f in the definition).
%Y A066495 Cf. also A109226, A138042, A227419.
%K A066495 nonn
%O A066495 1,1
%A A066495 _Joseph L. Pe_, Jan 03 2002
%E A066495 Extended by _Ray Chandler_, Aug 23 2005