A359500 a(n) = (7^2^n - 1)/2^(n+3).

3, 75, 90075, 259632270075, 4314170602515315024630075, 2382344702413741601833152075318304337413311121350075, 1452944967966417671787414728262962471027692106596483349510252251060925112718067382475349181570930962790075

Offset: 1

Author

Jianing Song, Jan 03 2023

Keywords

• nonn
• easy

Links

• Jianing Song, Table of n, a(n) for n = 1..10

Crossrefs

A261066 is twice this sequence.

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

Programs

PARI

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

Python

def A359500(n): return 7**(1<>n+3 # Chai Wah Wu, Jan 15 2023

Formula

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

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