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10 Points to TheExcalibur?, who gave the response |

10 Points to TheExcalabur?, who gave the response |

A post-closure hint from TheExcalibur? reads: |

A post-closure hint from TheExcalabur? reads: |

Ten points to TheExcalibur?, who gave the response |

Ten points to TheExcalabur?, who gave the response |

Status: *Closed*

10 Points to TheExcalabur?, who gave the response

- "n^n, for n=1,2,3, ...,

- Therefore, the next few are: 823543, 16777216, 387420489, 10000000000"

**Sequence #1: -2, 0, 4, 10, 18, 28, 40, 54, 70, 88, ...**

Status: *Closed*

10 Points to Smith, who gave the response

- "The next six terms are 108, 130, 154, 180, 208,238...

- The i-th term of n= (2i-2) + previous n, where the first term of n is defined as -2."

**Sequence #2: 0, 0, 1, 1, 3, 1, 3, 1, 3, 1, 7, 1, 3, 3, 3, 1, 3, 3, 9, 1, 3, 9, 5, 1, 3, 9, 9, 9, 19, 1, 27, ...**

Status: *Open*

**Sequence #3: 0.4612695550..., 0.4450853368..., 0.4305349047..., 0.4173569528..., 0.4053456945..., 0.3943364654..., 0.3841956640..., 0.3748135580..., 0.3660990370..., 0.3579757153..., 0.3503789912..., ...**

Status: *Open*

**Sequence #4: 0, 0, 1, 1, 3, 1, 5, 3, 5, 3, 9, 3, 11, 5, 7, 7, 15, 5, 17, ...**

Status: *Closed*

Ten points to Gobleteer, who gave the response

"7, 11, 9, 21, 7, 19"

A post-closure hint from TheExcalabur? reads:

"The number of numbers relatively prime to n, not including one, or equivilantly Sloan's A000010 - 1." I think this function might be worth keeping in mind for future problems.

**Sequence #5: 1/2, 1, 1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, ...**

Status: *Closed*

Ten points to TheExcalabur?, who gave the response

"One half of the difference between the nth and (n+1)th primes. (Sloan's A001223)

The next six items are 3, 1, 3, 2, 1, 3"

**Sequence #6: 0, 13, 6, 17, 24, 6, 17, 0, 18, 18, ...**

Status: *Open*

**Sequence #7: 0, 1, 0, 2, 0, 2, 0, 4, 0, 4, 0, 4, 0, 6, 0, 8, 0, ...**

Status: *Closed*

Ten points to TheExcalibur?, who gave the response

"For odd n: 0 For even n: Sloan's A062570, the number of solutions of x^2 - y^2 = 1 mod n/2

Then the next 6 items are 6, 0, 8, 0, 10, 0..."

**Sequence #8: 3, 7/5, 10/11, 5/6, 29/11, 155/77, 224/55 ...**

Status: *Open*

**Sequence #8': 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, ...**

Status: *Closed*

Closed by Gobleteer.

**Sequence #9: 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, ...**

Status: *Open*

**Sequence #10: 1, 9, 64, 1250, 7776, 352947, 4194304, 129140163, 2000000000, ...**

Status: *Closed*

Ten points to Paladin, who gave the response:

"129687123005 1486016741376 139788510734886 2381144319762432 116771704101562500 4611686018427387904

s[i] = (count numbers <= n and prime to n) / 2 (http://www.research.att.com/projects/OEIS?Anum=A000010)

x[i] = (i+1) ^ (i) * s[i]"