login
Index of first occurrence of n in the spiral shown in A274641.
3

%I #10 Feb 01 2025 23:15:15

%S 0,1,2,3,7,8,26,27,30,34,35,48,55,62,63,80,101,119,130,131,155,180,

%T 210,224,253,254,271,303,305,321,322,323,419,483,504,505,568,571,573,

%U 624,649,650,728,755,810,812,840,898,953,954,956,957,959,960,1189

%N Index of first occurrence of n in the spiral shown in A274641.

%C Also index of first occurrence of n+1 in the spiral shown in A274640.

%H N. J. A. Sloane, <a href="/A324481/b324481.txt">Table of n, a(n) for n = 0..223</a>

%F Conjecture: a(n) = c(n)*n^2 with 0.32 <= c(n) <= 1 for all n, maybe lim c(n) ~ 0.4. - _M. F. Hasler_, Feb 01 2025

%o (Python) A324481 = lambda n: next(i for i,a in enumerate(A274640()) if a==n+1) # slow

%o (Python)

%o def A324481(): # generator of the sequence

%o n=1

%o for i,a in enumerate(A274640()):

%o if a==n: yield i; n += 1

%o [a for a,_ in zip(A324481(),range(99))] # _M. F. Hasler_, Feb 01 2025

%Y Cf. A274640, A274641.

%K nonn,changed

%O 0,3

%A _N. J. A. Sloane_, Mar 11 2019