A095732 Sum of A095734(p) for all primes p such that Fib(n+1) <= p < Fib(n+2) (where Fib = A000045).

0, 0, 1, 3, 1, 3, 7, 10, 12, 23, 31, 58, 93, 171, 243, 422, 634, 1142, 1684, 2971, 4406, 7768, 11502, 20502, 30242, 53039, 79161, 138410, 207536, 362391, 544895, 947189, 1431794, 2473232, 3749944, 6459373, 9823917, 16879245, 25745781, 44112347

Offset

1,4

Comments

Ratio a(n)/A095354(n) converges as follows: 1, 1, 1, 1.5, 1, 1, 2.333333, 2, 1.714286, 2.090909, 1.9375, 2.416667, 2.513514, 3.109091, 2.892857, 3.349206, 3.20202, 3.845118, 3.676856, 4.22017, 4.053358, 4.640382, 4.420446, 5.088608, 4.828676, 5.446601, 5.212762, 5.838853, 5.611963, 6.257939, 6.017615, 6.668795, 6.424778, 7.069164, 6.819283, 7.467319, 7.215081, 7.868411, 7.614126, 8.269242

Links

Table of n, a(n) for n=1..40.

A. Karttunen, J. Moyer: C-program for computing the initial terms of this sequence

Example

a(1) = a(2) = 0, as there are no primes in ranges [1,2[ and [2,3[. a(3)=1 as in [3,5[ there is prime 3 with Fibonacci-representation 100, which is just a one fibit-flip away from being a palindrome (i.e. A095734(3)=1). a(4)=3, as in [5,8[ there are primes 5 and 7, whose Fibonacci-representations are 1000 and 1010 respectively and the other needs one bit-flip and the other two to become palindromes and 1 + 2 = 3. a(5)=1, as in [8,13[ there is only one prime 11, with Zeckendorf-representation 10100, which needs to have just its least significant fibit flipped from 0 to 1 to become palindrome.

Crossrefs

Cf. A095730, A095731, A095742 (sums of similar assymetricity measures for binary-expansion).

Sequence in context: A064434 A328988 A086401 * A001644 A139123 A133580

Adjacent sequences: A095729 A095730 A095731 * A095733 A095734 A095735

Keyword

nonn

Author

Antti Karttunen, Jun 12 2004

Status

approved