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A178482 Phi-antipalindromic numbers 5
1, 3, 4, 7, 8, 10, 11, 18, 19, 21, 22, 25, 26, 28, 29, 47, 48, 50, 51, 54, 55, 57, 58, 65, 66, 68, 69, 72, 73, 75, 76, 123, 124, 126, 127, 130, 131, 133, 134, 141, 142, 144, 145, 148, 149, 151, 152, 170, 171, 173, 174 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

We call m a phi-antipalindromic number if for the vector (a,...,b) (a<...<b) of exponents of its base-phi expansion, we have (a,...,b)=(-b,...,-a). For n>=2, either a(n)+1 or a(n)-1 is in the sequence; also either a(n)+3 or a(n)-3 is in the sequence.

Conjecture: this is the sequence of numbers k for which f(k) is an integer, where f(x) is the change-of-base function defined at A214969 using b=phi and c=b^2. [Clark Kimberling, Oct 17 2012]

LINKS

R. J. Mathar, Table of n, a(n) for n=1..3071.

FORMULA

For k>=1, a(2^k)=A005248(k); if 2^k<n<2^(k+1), then a(n)=a(2^k)+a(n-2^k).

EXAMPLE

The vectors of exponents of 4 and 5 are (-2,0,2) and (-4,-1,3) correspondingly (cf.A104605). Therefore by definition 4 is a phi-antipalindromic number, while 5 is not. Let n=38. Then k=5. Thus a(38)=A005248(5)+a(6)=123+10=133. The vector of exponents of phi in the base-phi expansion of 133 is (-10,-4,-2,2,4,10).

CROSSREFS

Cf. A005248 A055778 A104605 A104626 A104627 A104628

For bisections see A171070, A171071.

Sequence in context: A184823 A242921 A091934 * A024515 A187835 A184820

Adjacent sequences:  A178479 A178480 A178481 * A178483 A178484 A178485

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, May 28 2010, May 29 2010

STATUS

approved

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Last modified March 29 15:04 EDT 2017. Contains 284272 sequences.