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A059791
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Numbers n such that floor(phi^n) is prime, where phi = golden ratio.
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3
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2, 5, 6, 7, 11, 13, 17, 19, 24, 31, 37, 41, 47, 48, 53, 61, 71, 79, 96, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, 10691, 12251, 13963, 14449, 19469, 35449, 36779, 44507, 51169, 56003, 81671, 89849, 94823, 140057, 148091, 159521, 183089, 193201, 202667
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internal format)
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OFFSET
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1,1
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COMMENTS
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LINKS
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Eric Weisstein's World of Mathematics, Phi-Prime
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EXAMPLE
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floor(phi^863)=227160876495918562748535035942584201965901433059749617\
427535706949917136103176482875403653972639455945062095866005032008819\
9236184776437699830957031191632116265394965429613743580479 is prime.
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MATHEMATICA
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Block[{$MaxExtraPrecision=10000}, Select[Range[14000], PrimeQ[ Floor[ GoldenRatio^#]]&]] (* Harvey P. Dale, Mar 06 2017 *)
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PROG
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(PARI) isok(n) = isprime(floor(((sqrt(5)+1)/2)^n)) \\ Michel Marcus, Jul 14 2013
Terms generated and tested with pfgw then verified with PARI using the following:
(PARI) c(n) = 3*fibonacci(n-1) + fibonacci(n-2) + (n % 2) - 1; ispseudoprime(c(n)) \\ Mark Rodenkirch, Feb 27 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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