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

Jonathan Post jvospost3 at gmail.com
Mon Sep 6 19:34:03 CEST 2010

```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

```