A273340 Smallest base b such that A273339(b) = A002808(n); i.e., smallest base b > 1 such that the n-th composite number is the smallest "non-Wieferich pseudoprime" to base b, or -1 if no such b exists.

2, 17, 145, 577, 5185, -1, 19601

Offset

1,1

Comments

a(9) = 6350401, a(13) = 25401601.

Links

Table of n, a(n) for n=1..7.

Example

For n = 6, the sixth composite is 12. If A273339(x) is not 4 or 6, then x == 1 (mod 16) and x == 1 (mod 36), which implies x == 1 (mod 12^2), and so A273339(x) can't be 12. Therefore a(6) must be -1.

Prog

(PARI) composite(n) = my(i=0, c=2); while(1, if(!ispseudoprime(c), i++); if(i==n, return(c)); c++)
a273339(n) = forcomposite(c=1, , if(Mod(n, c^2)^(c-1)!=1, return(c)))
a(n) = my(b=2, c=composite(n)); while(a273339(b)!=c, b++); b

Crossrefs

Cf. A002808, A273339.

Sequence in context: A037636 A163066 A110815 * A074624 A374377 A245807

Adjacent sequences: A273337 A273338 A273339 * A273341 A273342 A273343

Keyword

sign,more

Author

Felix Fröhlich, May 20 2016

Extensions

a(6)-a(7) from Robert Israel, Aug 15 2025

Status

approved