OFFSET
1,2
COMMENTS
The matrix M in the definition of A292625 is given by this sequence, also, for each natural number m and each natural number c, ((2^(m+1)+1)^c-1)*(the product of any (m+1) not necessarily distinct terms of the m-th row) is palindromic in base (2^(m+1)+1), see the MathOverflow link. - Ahmad J. Masad, Apr 19 2023
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1275
Ahmad J. Masad, Conjecture on palindromic numbers, MathOverflow, Apr 2018.
EXAMPLE
The array begins:
1 3 13 63 313
1 5 41 365
1 9 145
1 17
1
Example of the result concerning palindromic numbers:
Take m=2, c=4, 2^(m+1) + 1 = 2^3 + 1 = 9, we choose 3 not necessarily distinct terms from the second row. Let them be 41, 365, 365; then we get 41*365*365*(9^4 - 1) = 35832196000 = 112435534211_9, which is a palindromic number in base 9.
MATHEMATICA
T[n_, k_] := ((2^(n + 1) + 1)^(k - 1) + 1)/2; Table[T[k, n - k + 1], {n, 1, 10}, {k, 1, n}] // Flatten (* Amiram Eldar, Sep 14 2022 *)
PROG
(PARI) tabl(n) = matrix(n, n, i, j, ((2^(i+1)+1)^(j-1)+1)/2); \\ Michel Marcus, Jan 02 2016
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ahmad J. Masad, Jan 01 2016
EXTENSIONS
a(31) corrected by Georg Fischer, Nov 07 2021
STATUS
approved