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A159556
Numbers that are the sum of distinct Fibonacci primes.
1
2, 3, 5, 7, 8, 10, 13, 15, 16, 18, 20, 21, 23, 89, 91, 92, 94, 96, 97, 99, 102, 104, 105, 107, 109, 110, 112, 233, 235, 236, 238, 240, 241, 243, 246, 248, 249, 251, 253, 254, 256, 322, 324, 325, 327, 329, 330, 332, 335, 337, 338, 340, 342, 343, 345, 1597, 1599, 1600
OFFSET
1,1
LINKS
EXAMPLE
For example: 7 = 5 + 2; 2 and 5 are Fibonacci numbers which are prime.
MAPLE
fibprimes:= select(isprime, [2, 3, seq(combinat:-fibonacci(ithprime(i)), i=3..100)]):
S:= expand(mul(1+x^p, p = fibprimes[1..11])):
sort(convert(map2(op, 2, indets(S, `^`)), list)): # Robert Israel, Jul 16 2015
MATHEMATICA
Union[Plus@@@Subsets[{2, 3, 5, 13, 89, 233, 1597}]] (* T. D. Noe, Apr 16 2009 *)
fibPrime={2, 3, 5, 13, 89, 233, 1597}; t=Rest[CoefficientList[Series[Product[1+x^fibPrime[[k]], {k, Length[fibPrime]}], {x, 0, fibPrime[[ -1]]}], x]]; Flatten[Position[t, _?(#>0&)]] (* T. D. Noe, Apr 15 2009 *)
PROG
(C) #include <stdio.h>
#define MAX_FIB 6
#define MAX_CALC 2580
int main() {
int fibs[] = {2, 3, 5, 13, 89, 233, 1597};
int num = 0;
int x = 0;
int index = 0;
for(x=1; x<MAX_CALC; x++) {
num = x;
for(index=MAX_FIB; index>-1; index--)
if(fibs[index]<=num) num-=fibs[index];
if(num==0) printf("%d, ", x);
}
printf("\n");
return 0;
}
CROSSREFS
Cf. A005478 (Fibonacci primes).
Sequence in context: A083027 A060107 A333230 * A219643 A194798 A302245
KEYWORD
nonn
AUTHOR
Jose Manuel Hernandez Jr. (j.hernandez38(AT)umiami.edu), Apr 14 2009
EXTENSIONS
Name corrected by T. D. Noe, Apr 15 2009
STATUS
approved