A227419 -id:A227419

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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).

+10
6

4, 9, 15, 21, 51, 71, 118, 184, 208, 227, 231, 238, 255, 267, 290, 317, 326, 354, 381, 392, 396, 437, 494, 499, 544, 553, 569, 627, 645, 660, 720, 756, 796, 922, 932, 937, 960, 968, 990, 1027, 1034, 1087, 1103, 1130, 1157, 1173, 1175, 1227, 1237, 1251

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A138042(n) + 2 [based on the formula found from A138042]. - Antti Karttunen, Jul 13 2013

EXAMPLE

f(9) = 6 = 4 + 2 = f(8) + f(7); so 9 is a term.

MATHEMATICA

f[n_] := Prime[n + 1] - Prime[n]; Select[Range[3, 10^4], f[ # ] == f[ # - 1] + f[ # - 2] &]

PROG

(Scheme with Antti Karttunen's IntSeq-library)

(define A066495 (MATCHING-POS 1 1 (lambda (n) (and (> n 2) (= (A001223 n) (+ (A001223 (- n 1)) (A001223 (- n 2))))))))

(define (A066495v2 n) (+ 2 (A138042 n))) ;; Alternative definition.

CROSSREFS

Cf. A000040 (function p in the definition).

Cf. A001223 (function f in the definition).

Cf. also A109226, A138042, A227419.

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Jan 03 2002

EXTENSIONS

Extended by Ray Chandler, Aug 23 2005

STATUS

approved

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