A098650 Smallest odd pseudoprime k > b to bases p_i, i.e., the smallest composite number k > b such that p_i^(k-1)-1 is divisible by k, p_i are the prime factors of b, where b is the n-th squarefree number, A005117(n).

9, 341, 91, 217, 1105, 25, 561, 15, 21, 561, 1541, 45, 45, 703, 645, 33, 561, 35, 1729, 49, 703, 1729, 561, 45, 561, 1891, 105, 1105, 77, 341, 65, 91, 65, 1729, 1105, 341, 87, 91, 561, 561, 1105, 85, 91, 561, 105, 111, 561, 703, 2465, 91, 561, 105, 781, 561, 91

Offset

1,1

References

Paulo Ribenboim, The New Book of Prime Number Records, New York: Springer-Verlag, p. 100, 1996.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for sequences related to pseudoprimes

Example

A005117(5) = 6 = 2*3. a(5) = 1105 because 1105 is the smallest psp to both bases 2 and 3.

Mathematica

PrimeFactors[ n_ ] := Flatten[ Table[ # [[ 1 ]], {1} ] & /@ FactorInteger[ n ]]; f[n_] := Block[{k = n + 1}, If[ EvenQ[k], k++ ]; While[ PrimeQ[k] || Union[ PowerMod[ PrimeFactors[n], k - 1, k]] != {1}, k += 2]; k]; f /@ Select[ Range[90], SquareFreeQ[ # ] &]

Prog

(PARI) lista(nn) = my(f, k); for(b=1, nn, if(issquarefree(b), f=factor(b)[, 1]; k=b+1+b%2; while(isprime(k) || sum(i=1, #f, Mod(f[i], k)^(k-1)==1)<#f, k+=2); print1(k, ", "))); \\ Jinyuan Wang, Jul 24 2021

Crossrefs

Cf. A005117, A007535, A098651 (indices of records), A098652 (records).

Sequence in context: A152553 A090087 A090085 * A354689 A098652 A110695

Adjacent sequences: A098647 A098648 A098649 * A098651 A098652 A098653

Keyword

nonn

Author

Robert G. Wilson v, Sep 18 2004

Status

approved