A028562 -id:A028562 - cp's OEIS frontend

A185739 Accumulation array of A185738, by antidiagonals.

1, 3, 4, 6, 10, 11, 10, 18, 25, 26, 15, 28, 42, 56, 57, 21, 40, 62, 90, 119, 120, 28, 54, 85, 128, 186, 246, 247, 36, 70, 111, 170, 258, 378, 501, 502, 45, 88, 140, 216, 335, 516, 762, 1012, 1013, 55, 108, 172, 266, 417, 660, 1030, 1530, 2035, 2036, 66, 130, 207, 320, 504, 810, 1305, 2056, 3066, 4082, 4083, 78, 154, 245, 378, 596, 966, 1587, 2590, 4106, 6138, 8177, 8178, 91

Offset: 1

Clark Kimberling, Feb 02 2011

This arrays is a member of a chain; see A185738.

			Northwest corner:
1....3....6....10....15
4....10...18...28....40
11...25...42...62....85
26...56...90...128...170

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Rows 1 to 4: A000217, A028562, A140675, 2*A098847
Columns 1 to 3: A000295, A000247, A068293.
Cf. A185738, A185740.

(* See A185738 *)
f[n_, k_] := (k/2)*(4*(2^n - 1) + (k - 3)*n);
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 10}]]  (* Array A185739 *)
Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 11 2017 *)

T(n,k) = k*(4*(2^n-1)+(k-3)*n), k>=1, n>=1.

A028561 Numbers k such that k*(k+6) is a palindrome.

Original entry on oeis.org

0, 1, 5, 22, 137, 273, 715, 863, 2731, 8541, 486618, 877173, 1378507, 1731746, 2273915, 2436099, 5401396, 7153679, 7560069, 14529486, 23887419, 23975475, 73114035, 84890503, 88837611, 235680755, 235769755, 272515513, 440021417, 782357262, 1414071397, 2352019439

Offset: 1

Patrick De Geest

Michael S. Branicky, Table of n, a(n) for n = 1..35
Patrick De Geest, Palindromic Quasipronics of the form n(n+x)
Erich Friedman, What's Special About This Number? (See entries 863, 8541.)

Cf. A002113, A028560, A028562.

Select[Range[0,24*10^6],PalindromeQ[#(#+6)]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 04 2017 *)

from itertools import count, islice
def ispal(n): s = str(n); return s == s[::-1]
def agen():
    for k in count(0):
        if ispal(k*(k+6)):
            yield k
print(list(islice(agen(), 22))) # Michael S. Branicky, Jan 25 2022

a(23) and beyond from Michael S. Branicky, Jan 25 2022

cp's OEIS Frontend

A185739 Accumulation array of A185738, by antidiagonals.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula