login
a(n) = (7^2^n - 1)/2^(n+3).
2

%I #18 Feb 10 2025 20:49:10

%S 3,75,90075,259632270075,4314170602515315024630075,

%T 2382344702413741601833152075318304337413311121350075,

%U 1452944967966417671787414728262962471027692106596483349510252251060925112718067382475349181570930962790075

%N a(n) = (7^2^n - 1)/2^(n+3).

%H Jianing Song, <a href="/A359500/b359500.txt">Table of n, a(n) for n = 1..10</a>

%F a(n)/a(n-1) = (7^2^(n-1) + 1)/2 = 2^(n+1) * a(n-1) + 1.

%F For all n > m, a(n) and a(m) are congruent modulo 2^(m+2) but not modulo 2^(m+3).

%o (PARI) a(n) = (7^2^n - 1)/2^(n+3)

%o (Python)

%o def A359500(n): return 7**(1<<n)-1>>n+3 # _Chai Wah Wu_, Jan 15 2023

%Y A261066 is twice this sequence.

%Y Cf. {odd part of m^2^n - 1}: A068531 (m=3 or m=9), A097421 (m=5), this sequence (m=7).

%K nonn,easy

%O 1,1

%A _Jianing Song_, Jan 03 2023