COMMENTS
The nontrivial squares of the form a + 2b + c where a, b and c are consecutive numbers in consecutive bases: (4 + 8 + 8 + 16 = 36, 9 + 27 + 27 + 81 = 144). - Steve Homewood, Feb 11 2023
Discussion
Sat Feb 11
15:52
Jon E. Schoenfield: By “consecutive numbers in consecutive bases”, do you mean consecutive powers of a given base? I’m having trouble understanding the wording used in the Comments entry.
15:57
Andrew Howroyd: I can't see this as anything other than an incomprehensible transcription of the first formula. n^2*(n-1)^2 or b^2*(1 + 2*b + b^2) where b = n-1. I suggest to reject.
16:01
Jon E. Schoenfield: Yes, I was about to ask: Is it true that your variables a, b, and c are given by a = (n-1)^2, b = (n-1)^3, and c= (n-1)^4, so the n-th term of the sequence is a + 2b + c = ((n-1) + (n-1)^2)^2 = ((n-1)*(1+(n-1)))^2 = ((n-1)*(1+n-1))^2 = ((n-1)*n)^2?
16:02
Jon E. Schoenfield: But Andrew beat me to it (and put it much better than I did).
16:03
Steve Homewood: Consecutive powers is a lot more clearer. Taking a + 2b + c where a,b and c are consecutive powers then the square of any base added to twice the cube plus the fourth power is always a square number and those squares are in this sequence, 36, 144, 400, 900.....
16:03
Jon E. Schoenfield: I’m sorry, but I have to agree that this proposed Comments entry should be rejected. :-(
16:07
Steve Homewood: Ok then, reject it.
Tue Feb 14
01:19
Jon E. Schoenfield: Do any other editors want to weigh in?
COMMENTS
The nontrivial squares of the form a + 2b + c where a, b and c are consecutive numbers in consecutive bases:- (4 + 8 + 8 + 16 = 36, 9 + 27 + 27 + 81 = 144). - Steve Homewood, Feb 11 2023
COMMENTS
The non-trivial nontrivial squares of the form a + 2b + c where a,b and c are consecutive numbers in consecutive bases:- (4 + 8 + 8 + 16 = 36, 9 + 27 + 27 + 81 = 144). - Steve Homewood, Feb 11 2023
Discussion
Sat Feb 11
15:48
Jon E. Schoenfield: Spelling corrected per the OEIS Style Sheet; for more information, see https://oeis.org/wiki/Style_Sheet#Spelling_and_notation
Discussion
Sat Feb 11
15:25
Andrew Howroyd: (i see that they are 3^2, 3^3, 3^4, but why is this as described?)
15:41
Steve Homewood: 2^2 + 2^3 + 2^3 + 2^4 = 36, 3^2 + 3^3 + 3^3 + 3^4 = 144, base 2 and base 3 consecutively. 4^2 + 4^3 + 4^3 + 4^4 = 400 and 5^2 + 5^3 + 5^3 + 5^4 = 900, in base 4 and base 5. The rest of the numbers are produced for base 6, base 7, base 8, base 9, base 10 ad infinitum.
COMMENTS
The non-trivial squares of the form a + 2b + c where a,b and c are consecutive numbers in consecutive bases:- (4 + 8 + 8 + 16 = 36, 9 + 27 + 27 + 81 = 144) _. - _Steve Homewood_, Feb 11 2023
Discussion
Sat Feb 11
15:23
Andrew Howroyd: I don't quite follow why 9, 27, 81 are consecutive numbers in consecutive bases.
COMMENTS
The non-trivial squares of the form a + 2b + c where a,b and c are consecutive numbers in consecutive bases:- (4 + 8 + 8 + 16 = 36, 9 + 27 + 27 + 81 = 144) _Steve Homewood_, Feb 11 2023
Discussion
Sat Feb 11
15:03
Jon E. Schoenfield: Your signature format is incorrect. Please see https://oeis.org/wiki/Style_Sheet#Signing_your_name_when_you_contribute_to_an_existing_sequence
