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A169791 Least number k having n distinct representations as the sum of a nonzero Fibonacci number and a prime. 2
9, 3, 4, 8, 24, 74, 444, 1614, 15684, 29400, 50124, 556274, 5332128, 11110428, 50395440, 509562294, 1296895890, 13314115434, 187660997904, 326585290794, 4788143252148 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

We count ordered index pairs (i,j) that represent k = Fibonacci(i) + prime(j), i >= 1, j >= 1.

A variant of A168382, because Fibonacci(1)=1 and Fibonacci(2)=1 may both contribute individually to the count.

Fibonacci(1) + prime(4) = Fibonacci(2) + prime(4) = Fibonacci(4) + prime(3) = Fibonacci(5) + prime(2) = 8 are four "distinct" representations of k=8, because Fibonacci(1) = Fibonacci(2) are treated as distinguishable.

a(18) > 10^10. [Donovan Johnson, May 17 2010]

Except for a(1), all terms appear to be of the form p+1 for some prime p. - Chai Wah Wu, Dec 06 2019

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

1+443 = 1+443 = 5+439 = 13+431 = 55+389 = 233+211 = 377+67 are n=7 distinct representations of k=444.

CROSSREFS

Cf. A168382, A169790.

Sequence in context: A102754 A225455 A154184 * A275519 A196996 A154978

Adjacent sequences:  A169788 A169789 A169790 * A169792 A169793 A169794

KEYWORD

nonn,more

AUTHOR

R. J. Mathar and Jon E. Schoenfield, May 14 2010

EXTENSIONS

a(12)-a(15) from Max Alekseyev, May 15 2010

a(16)-a(17) from Donovan Johnson, May 17 2010

A prime index in the comment corrected by R. J. Mathar, Jun 02 2010

a(18) from Chai Wah Wu, Dec 06 2019

a(19)-a(21) from Giovanni Resta, Dec 10 2019

STATUS

approved

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Last modified June 29 17:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)