A275392 Smallest term in the tribonacci Zeckendorf representation of n.

1, 2, 1, 4, 1, 2, 7, 1, 2, 1, 4, 1, 13, 1, 2, 1, 4, 1, 2, 7, 1, 2, 1, 24, 1, 2, 1, 4, 1, 2, 7, 1, 2, 1, 4, 1, 13, 1, 2, 1, 4, 1, 2, 44, 1, 2, 1, 4, 1, 2, 7, 1, 2, 1, 4, 1, 13, 1, 2, 1, 4, 1, 2, 7, 1, 2, 1, 24, 1, 2, 1, 4, 1, 2, 7, 1, 2, 1, 4, 1, 81, 1, 2, 1, 4, 1, 2, 7, 1, 2, 1, 4, 1, 13, 1, 2, 1, 4, 1, 2, 7, 1, 2, 1

Offset: 1

Author

Aresh Pourkavoos, Jul 26 2016

Keywords

• nonn

Examples

			The tribonacci Zeckendorf representation of 5 is 4+1 (4 and 1 are both tribonacci numbers), the smaller term of which is 1, so a(5)=1.
		

Links

• Aresh Pourkavoos, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A000073, A006519, A139764.

Programs

Python

tribonacci = [0, 0, 1]
seq = []
numTerms = 100
while tribonacci[-1] < numTerms:
  tribonacci.append(tribonacci[-1]+tribonacci[-2]+tribonacci[-3])
tribonacci = tribonacci[3:]
tribonacci.reverse()
for n in range(1, numTerms):
  tmp = n
  smallestTerm = 0
  for place in tribonacci:
    if tmp >= place:
      tmp -= place
      smallestTerm = place
  seq.append(str(n)+" "+str(smallestTerm))
print('\n'.join(seq))

Formula

a(n) = n if n is in A000073.