The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A258929

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A258929

a(n) is the unique even-valued residue modulo 5^n of a number m such that m^2+1 is divisible by 5^n.
(history; published version)

#11 by N. J. A. Sloane at Tue Jun 23 00:52:52 EDT 2015

STATUS

proposed

approved

#10 by Jon E. Schoenfield at Tue Jun 23 00:19:27 EDT 2015

STATUS

editing

proposed

#9 by Jon E. Schoenfield at Tue Jun 23 00:18:52 EDT 2015

CROSSREFS

Cf. A048898, A048899, A257366, A259266.

#8 by Jon E. Schoenfield at Tue Jun 23 00:16:35 EDT 2015

COMMENTS

For any positive integer n, if a number of the form m^2+1 is divisible by 5^n, then m mod 5^n must take one of two values--one even, the other odd. This sequence gives the even residue. (The odd residues are in A259266.)

CROSSREFS

Cf. A257366, A259266.

EXTENSIONS

More terms and additional comments from Jon E. Schoenfield, Jun 23 2015

#7 by Jon E. Schoenfield at Tue Jun 23 00:08:16 EDT 2015

NAME

a(n) is the unique even-valued residue modulo- 5^n residue of a number m such that m^2+1 is divisible by 5^n.

DATA

2, 18, 68, 182, 1068, 1068, 32318, 280182, 280182, 3626068, 23157318, 120813568, 1097376068, 1097376068, 11109655182, 49925501068, 355101282318, 355101282318, 15613890344818, 15613890344818, 365855836217682, 2273204469030182, 2273204469030182, 49956920289342682

STATUS

approved

editing

#6 by N. J. A. Sloane at Sun Jun 21 11:23:31 EDT 2015

STATUS

proposed

approved

#5 by Jon E. Schoenfield at Mon Jun 15 01:18:23 EDT 2015

STATUS

editing

proposed

Discussion

Mon Jun 15

07:59

Joerg Arndt: "modulo-5^n residue" --> "residue modulo 5^n" ?

Tue Jun 16

22:33

Jon E. Schoenfield: I think I'd rather just recycle it ... I apologize for taking up your time with it.  :-(

Thu Jun 18

08:41

Joerg Arndt: Strongly suggest to keep both of your new sequences.

#4 by Jon E. Schoenfield at Mon Jun 15 01:18:17 EDT 2015

STATUS

proposed

editing

#3 by Jon E. Schoenfield at Mon Jun 15 01:12:27 EDT 2015

STATUS

editing

proposed

Discussion

Mon Jun 15

01:18

Jon E. Schoenfield: I'm sorry ... I just now found A048898 and A048899 (whose terms would be intertwined with this one and the related sequence of odd residues), and I think that, collectively, this one and the proposed sequence of odd residues are redundant with those two existing sequences.

Suggest recycling this one.  :-(

#2 by Jon E. Schoenfield at Mon Jun 15 01:07:23 EDT 2015

NAME

allocated for Jon E. Schoenfield

a(n) is the unique even-valued modulo-5^n residue of a number m such that m^2+1 is divisible by 5^n.

DATA

2, 18, 68, 182, 1068, 1068, 32318, 280182, 280182, 3626068, 23157318, 120813568, 1097376068, 1097376068, 11109655182, 49925501068, 355101282318, 355101282318, 15613890344818, 15613890344818

OFFSET

1,1

COMMENTS

For any positive integer n, if a number of the form m^2+1 is divisible by 5^n, then m mod 5^n must take one of two values--one even, the other odd. This sequence gives the even residue.

EXAMPLE

If m^2+1 is divisible by 5, then m mod 5 is either 2 or 3; the even value is 2, so a(1)=2.

If m^2+1 is divisible by 5^2, then m mod 5^2 is either 7 or 18; the even value is 18, so a(2)=18.

If m^2+1 is divisible by 5^3, then m mod 5^3 is either 57 or 68; the even value is 68, so a(3)=68.

CROSSREFS

Cf. A257366.

KEYWORD

allocated

nonn

AUTHOR

Jon E. Schoenfield, Jun 15 2015

STATUS

approved

editing

Discussion

Mon Jun 15

01:12

Jon E. Schoenfield: Does this look worth including in the OEIS?  If so, I can add more terms and one other sequence listing the odd residues.