A097421 -id:A097421 - cp's OEIS frontend

A261066 a(n) = (7^(2^n) - 1) / 2^(n+2).

6, 150, 180150, 519264540150, 8628341205030630049260150, 4764689404827483203666304150636608674826622242700150

Offset: 1

Marco Ripà, Aug 08 2015

nonn

(m^(2^n)-1)/2^(n+2) is an integer for any odd value of m and n>0.

The next term, a(7), has 106 decimal digits.

			a(3) = (7^8 - 1)/2^5 = 180150.

Cf. A059723, A068531, A097421. Twice A359500.

[(7^(2^n)-1)/2^(n+2): n in [1..10]]; // Vincenzo Librandi, Aug 09 2015

Table[(7^(2^n) - 1)/2^(n + 2), {n, 1, 7}] (* Vincenzo Librandi, Aug 09 2015 *)

first(m)=vector(m,i, (7^(2^i)-1)/2^(i+2)); /* Anders Hellström, Aug 08 2015 */

A261066(n)=7^2^n>>(n+2) \\ M. F. Hasler, Aug 11 2015

a(n) == 150 (mod 10^4) for all n > 1. - M. F. Hasler, Aug 11 2015

a(5) corrected by Vincenzo Librandi, Aug 09 2015

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

Original entry on oeis.org

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

Offset: 1

Jianing Song, Jan 03 2023

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

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).

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

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

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).

A261067 a(n) = (11^(2^n) - 1)/2^(n + 2).

Original entry on oeis.org

15, 915, 6698715, 717964529118315, 16495138082306681918325119173515, 17413733142679306233865281770975943513633443105435651232476307915

Offset: 1

Marco Ripà, Aug 08 2015

(m^(2^n) - 1)/2^(n + 2) is an integer for any odd value of m and n > 0.

In particular, for m = 11, a(n) is a multiple of 15.

			a(3) = (11^8 - 1)/2^5 = 6698715.

Cf. A059723, A068531, A068533, A097421.

[(11^(2^n)-1)/2^(n+2): n in [1..6]]; // Vincenzo Librandi, Aug 14 2015

A261067:=n->(11^(2^n) - 1)/2^(n + 2): seq(A261067(n), n=1..8); # Wesley Ivan Hurt, Jan 27 2017

Table[(11^(2^n) - 1)/2^(n + 2), {n, 10}] (* Vincenzo Librandi, Aug 14 2015 *)

first(m)=vector(m,i, (11^(2^i)-1)/2^(i+2)); /* Anders Hellström, Aug 08 2015 */

a(n) = 15*A068533(n). - Michel Marcus, Aug 14 2015

cp's OEIS Frontend

A261066 a(n) = (7^(2^n) - 1) / 2^(n+2).

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

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A261067 a(n) = (11^(2^n) - 1)/2^(n + 2).

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Magma

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Mathematica

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