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Revision History for A355702

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A355702

a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of prime divisors as the sum a(n-2) + a(n-1).
(history; published version)

#12 by Michael De Vlieger at Sat Jul 23 09:54:27 EDT 2022

STATUS

proposed

approved

#11 by Scott R. Shannon at Sat Jul 23 09:29:09 EDT 2022

STATUS

editing

proposed

#10 by Scott R. Shannon at Sat Jul 23 09:24:19 EDT 2022

COMMENTS

In the first 500000 terms on seventeen occasions the sum of the previous two terms equals the next term, the first such these terms being 3, 5, 8, 11, 100, 320, 480. .. ,131072, 262144. It in unknown if there are infinitely many such terms. In the same range there are seventy-three fixed points; see A356017. The sequence is conjectured to be a permutation of the positive integers.

Discussion

Sat Jul 23

09:29

Scott R. Shannon: Submitting A355702 and A356017 together.

#9 by Scott R. Shannon at Sat Jul 23 09:22:01 EDT 2022

COMMENTS

In the first 500000 terms on seventeen occasions the sum of the previous two terms equals the next term, the first such terms being 3, 5, 8, 11, 100, 320, 480. It in unknown if there are infinitely many such terms. In the same range there are seventy-three fixed points. See Axxx; see A356017. The sequence is conjectured to be a permutation of the positive integers.

CROSSREFS

Cf. A356017, A001222, A355647, A355649, A352867.

#8 by Scott R. Shannon at Sat Jul 23 09:15:58 EDT 2022

COMMENTS

In the first 500000 terms on seventeen occasions the sum of the previous two terms equals the next term, the first such terms being 3, 5, 8, 11, 100, 320, 480. It in unknown if there are infinitely many such terms. In the same range there are seventy-three fixed points. See Axxx. The sequence is conjectured to be a permutation of the positive integers.

#7 by Scott R. Shannon at Sat Jul 23 09:11:44 EDT 2022

LINKS

Scott R. Shannon, <a href="/A355702/a355702_1.png">>Image of the first 500000 terms</a>. The green line is y = n.

#6 by Scott R. Shannon at Sat Jul 23 09:11:29 EDT 2022

LINKS

Scott R. Shannon, <a href="/A355702/a355702_1.png">>Image of the first 100000 500000 terms</a>. The green line is y = n.

#5 by Scott R. Shannon at Sat Jul 23 08:52:40 EDT 2022

NAME

wip

a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that has not yet appeared that has the same number of prime divisors as the sum a(n-2) + a(n-1).

EXAMPLE

a(4) = 5 as a(2) + a(3) = 2 + 3 = 5 which has one prime divisor, and 5 is the smallest unused number that has one prime divisor.

a(6) = 7 as a(4) + a(5) = 5 + 8 = 13 which has one prime divisor, and 7 is the smallest unused number that has one prime divisor.

a(7) = 4 as a(5) + a(6) = 8 + 7 = 15 which has two prime divisors, and 4 is the smallest unused number that has two prime divisors.

CROSSREFS

Cf. A001222, A355647, A355649, A352867.

#4 by Scott R. Shannon at Fri Jul 15 07:15:23 EDT 2022

LINKS

Scott R. Shannon, <a href="/A355702/a355702.png">Image of the first 100000 terms</a>. The green line is y = n.

Discussion

Fri Jul 22

12:29

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A355702 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

#3 by Scott R. Shannon at Fri Jul 15 07:14:19 EDT 2022

DATA

1, 2, 3, 5, 8, 7, 4, 11, 6, 13, 17, 12, 19, 23, 18, 29, 31, 16, 37, 41, 20, 43, 27, 28, 9, 47, 24, 53, 10, 30, 36, 42, 44, 14, 15, 59, 21, 32, 61, 22, 67, 71, 45, 50, 25, 52, 26, 63, 73, 40, 79, 33, 48, 54, 66, 72, 68, 56, 70, 60, 75, 81, 84, 76, 64, 88, 90, 34, 78, 80, 35, 38, 83, 39, 46, 49, 51