A182570 -id:A182570 - cp's OEIS frontend

A182569 Primes that have two terms in their Zeckendorf representation.

7, 11, 23, 29, 37, 47, 97, 149, 157, 199, 241, 379, 521, 613, 631, 1021, 1741, 2207, 3571, 9349, 10949, 11933, 17713, 46381, 46457, 46601, 50549, 75169, 196439, 203183, 214129, 560597, 832129, 2178343, 3010349, 3531343, 14930441, 15444581, 16276621, 24157961

Offset: 1

Alex Ratushnyak, May 05 2012

nonn

Primes of the form Fibonacci(x)+Fibonacci(y), x-y>1.

			7 = 5+2. 11=8+3. 23=21+2. 29 =21+8.

Cf. A014417, A179242-A179253, A182535, A182570-A182574.

nn = 40; f = Fibonacci[Range[nn]]; ps = {}; Do[ps = Union[ps, Select[f[[k]] + Delete[f, {{k-1}, {k}, {k+1}}], PrimeQ]], {k, 4, nn-1}]; ps (* T. D. Noe, May 08 2012 *)

Intersection of A000040 and A179242. - Michel Marcus, May 28 2013

More terms from T. D. Noe, May 08 2012

A182669 Floor-sum sequence of r, with r = golden ratio = (1+sqrt(5))/2 and a(1)=1, a(2)=3.

Original entry on oeis.org

1, 3, 6, 11, 14, 19, 22, 24, 27, 32, 35, 37, 40, 43, 45, 48, 53, 56, 58, 61, 64, 66, 69, 71, 74, 77, 79, 82, 87, 90, 92, 95, 98, 100, 103, 105, 108, 111, 113, 116, 119, 121, 124, 126, 129, 132, 134, 137, 139, 142, 145, 147, 150, 153, 155, 158, 160, 163, 166, 168, 171, 173, 174, 176, 179, 181, 184

Offset: 1

Clark Kimberling, Nov 27 2010

nonn

Let S be the set generated by these rules: (1) if m and n are in S and m

Let B be the Beatty sequence of r. Then a floor-sum sequence of r is a subsequence of B if and only if a(1) and a(2) are terms of B. Thus, A182669 is a subsequence of the lower Wythoff sequence, A000201.

			a(3)=floor(r+3r)=6.

Iain Fox, Table of n, a(n) for n = 1..3000

Cf. A000201, A182653, A182570.

lista(nn) = my(S=[1, 3], r=(1+sqrt(5))/2, new, k); while(1, new=[]; for(m=1, #S, for(n=m+1, #S, k=floor(r*(S[m]+S[n])); if(k<=nn, new=setunion(new,[k])))); if(S==setunion(S,new), return(S)); S=setunion(S,new)) \\ Iain Fox, Apr 25 2019

r=(1+5^(1/2))/2: s(1)=1: s(2)=3: s(5)=6
For h=2 to 200: c(h)=h+c(h-1): next h
For h=1 to 100: c=c(h): d=0
  For i=1 to h+1: d=d+1: s(c+d)=int(s(i)+s(h+2)*r)
  Next i
Next h
For i=1 to 1000: for j=i+1 to 1001
if s(i)>=s(j) then swap s(i),s(j)
next j,i
For i=1 to 120: if s(i+1)<>s(i) then print s(i);
next i

139 (generated by m=22, n=64) added by R. J. Mathar, Nov 28 2010

A182571 Primes that have four terms in their Zeckendorf representation.

Original entry on oeis.org

53, 67, 83, 101, 109, 127, 137, 139, 163, 193, 223, 263, 271, 277, 281, 283, 311, 317, 331, 337, 359, 389, 397, 409, 421, 439, 443, 461, 503, 547, 557, 563, 577, 641, 653, 659, 683, 691, 709, 761, 769, 811, 853, 857, 859, 911, 919, 937, 953, 1019, 1031, 1039

Offset: 1

Alex Ratushnyak, May 05 2012

nonn

Cf. A179242-A179253, A182535, A182569, A182570.

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A182569 Primes that have two terms in their Zeckendorf representation.

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A182669 Floor-sum sequence of r, with r = golden ratio = (1+sqrt(5))/2 and a(1)=1, a(2)=3.

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A182571 Primes that have four terms in their Zeckendorf representation.

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