A391075 - OEIS

%I #17 Nov 30 2025 14:24:59

%S 0,26,1,76,1,126,1,176,1,226,2,276,2,326,2,376,2,426,3,476,3,526,3,

%T 576,3,626,4,676,4,726,4,776,4,826,5,876,5,926,5,976,5,1026,6,1076,6,

%U 1126,6,1176,6,1226,7,1276,7,1326,7,1376,7,1426,8,1476,8,1526,8,1576,8,1626,9,1676,9,1726,9,1776,9,1826,10

%N a(n) = 25*n+1 if n is odd and floor((n+6)/8) if n is even.

%C Does iterating n -> a(n) always reach 1 (i.e., the cycle 1 -> 26 -> 4 -> 1)?

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,0,0,1,0,-1).

%F a(2*n+1) = a(2*n-1) + 50 for n > 0.

%F a(8*n) = a(8*n-2) = a(8*n-4) = a(8*n-6) for n > 0.

%F a(n) = a(n-2) + a(n-8) - a(n-10).

%F G.f.: (26*x + x^2 + 50*x^3 + 50*x^5 + 50*x^7 + 24*x^9) / ((1-x^2) * (1-x^8)).

%t a[n_] := If[OddQ[n], 25*n + 1, Floor[(n + 6)/8]]; Array[a, 100, 0] (* _Amiram Eldar_, Nov 27 2025 *)

%o (PARI) a(n) = if(n%2==0, floor((n+6)/8), 25*n+1)

%o (Python)

%o def A391075(n): return 25*n+1 if n&1 else n+6>>3 # _Chai Wah Wu_, Nov 30 2025

%Y Cf. A006370, A391054.

%K nonn,easy

%O 0,2

%A _Werner Schulte_, Nov 27 2025