A168383 Numbers expressible as the sum of a prime and a Fibonacci number in only one way, and such that the prime and Fibonacci number have the same number of decimal digits.
2, 9, 65, 77, 93, 95, 123, 323, 335, 343, 377, 395, 415, 425, 437, 527, 545, 553, 583, 586, 670, 700, 715, 723, 726, 731, 749, 783, 801, 804, 833, 838, 849, 851, 901, 903, 905, 906, 923, 957, 959, 964, 965, 1003, 1078, 1081, 1113, 1115
Offset: 1
Examples
In the decomposition of 1081, the prime and Fibonacci both have three digits: 1081 = 144 + 937.
References
- J. Earls, "Fibonacci Prime Decompositions," Mathematical Bliss, Pleroma Publications, 2009, pages 76-79. ASIN: B002ACVZ6O
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
filter:= proc(n) local f,i,d,state; state:= 0; for i from 0 do f:= combinat:-fibonacci(i); if f >= n then return (state = 1) fi; if isprime(n-f) then state:= state+1; if state = 2 then return false fi; if f = 0 then d:= 1 else d:= 1+ilog10(f) fi; if 1+ilog10(n-f) <> d then return false fi; fi od; end proc: select(filter, [$1..2000]); # Robert Israel, Aug 22 2024
Extensions
Definition clarified by Robert Israel, Aug 22 2024
Comments