# [seqfan] Re: After the trivial 341, what is the smallest pseudoprime A001567 in the Partial sums of pseudoprimes A001567?

Charles Greathouse charles.greathouse at case.edu
Tue Sep 7 04:54:06 CEST 2010

```There are no more 2-pseudoprime terms below 663433633517891440468203298.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

On Mon, Sep 6, 2010 at 1:34 PM, Jonathan Post <jvospost3 at gmail.com> wrote:
> I wonder. After the trivial 341, what is the smallest pseudoprime
> A001567 in the Partial sums of pseudoprimes A001567?
>
> A172255                  Partial sums of pseudoprimes A001567.
>
> 341, 902, 1547, 2652, 4039, 5768, 7673, 9720, 12185, 14886, 17707,
> 20984, 25017, 29386, 33757, 38438, 43899, 50500, 58457, 66778, 75259,
> 84170, 94431, 105016, 116321, 129122, 142863, 156610, 170591, 185082,
> 200791, 216632, 233337, 252042
>
>        OFFSET
> 1,1
>
>        COMMENT
>
> An odd composite number n is a Fermat pseudoprime to base b iff
> b^(n-1) == 1 mod n. Fermat pseudoprimes to base 2 are often simply
> called pseudoprimes, or Sarrus numbers. The subsequence of pseudoprime
> partial sum of pseudoprimes begins 341, and the next exceeds a(40).
> The subsequence of prime partial sum of pseudoprimes begins 7673,
> 17707, 33757, 270763.
>
>        FORMULA
> a(n) = SUM[i=1..n] {odd composite numbers n such that 2^(n-1) == 1 mod n}.
>
>        EXAMPLE
> a(15) = 341 + 561 + 645 + 1105 + 1387 + 1729 + 1905 + 2047 + 2465 +
> 2701 + 2821 + 3277 + 4033 + 4369 + 4371 = 33757 is prime.
>
>        CROSSREFS
>
> Cf. A000040, A001567.
>
>        KEYWORD
> easy,nonn
>
>        AUTHOR
> Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 29 2010
>
>
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>

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