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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A306450 Non-coprime pseudoprimes to base 3 (A306451) that are not squarefree.

Original entry on oeis.org

726, 1053426, 6498426, 7912311, 8141001, 190381521, 202730781, 283975626, 524245326, 767159481, 1095790641, 1620456321, 1904467521, 2287621281, 2700546486, 3462782961, 4120800321, 4928482581, 5816852481, 5974336401, 9313587921, 18723332001, 21215225361, 22073079666, 29882080866, 30132305841
Offset: 1

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Author

Jianing Song, Feb 16 2019

Keywords

Comments

Intersection of A306451 and A013929.
Terms must be divisible by the square of a Mirimanoff prime p (or base-3 Wieferich prime, A014127) such that the multiplicative order of 3 modulo p is not divisible by 3. So far, the only known Mirimanoff primes are 11 and 1006003. The multiplicative order of 3 modulo 11 is 5, not a multiple of 3, while the multiplicative order of 3 modulo 1006003 is 1006002, which is a multiple of 3. As a result, all known terms are divisible by 3*11^2 = 363.

Examples

			726 is a term because 726 divides 3^726 - 3 and 726 = 2 * 3 * 11^2.

Crossrefs

Cf. A295740, A244065, A306451, A306452.

Programs

  • PARI
    forstep(n=3, 10^9, 3, if(Mod(3, n)^n==3 && !issquarefree(n), print1(n, ", ")))

Extensions

More terms from Jinyuan Wang, Feb 18 2019
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