cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A384438 Composite numbers k such that ((2^k+1)/3)^k == 1 (mod k^2).

Original entry on oeis.org

341, 1105, 1387, 1729, 1771, 2047, 2465, 2485, 2701, 2821, 3277, 3445, 4033, 4369, 4681, 5185, 5461, 6601, 7957, 8321, 8911, 9361, 10261, 10585, 11305, 11713, 11891, 13741, 13747, 13981, 14491, 15709, 15841, 16105, 16705, 18145, 18721, 19951, 23377, 28441, 29341
Offset: 1

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Author

Thomas Ordowski, May 29 2025

Keywords

Comments

If p > 3 is prime, then ((2^p+1)/3)^p == 1 (mod p^2).
Fermat pseudoprimes to base 2 not divisible by 3 (A066488) are a proper subsequence.
The terms k that are not 2^(k-1) == 1 (mod k) are 1771, 2485, 3445, 5185, 9361, ...

Crossrefs

Cf. A001567, A066488 (subsequence), A384148.

Programs

  • PARI
    isok(k) = (k>1) && (k%2) && !isprime(k) && (Mod((2^k+1)/3, k^2)^k == 1); \\ Michel Marcus, May 29 2025

Extensions

a(18)-a(41) from Jinyuan Wang, May 29 2025
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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