A028553 -id:A028553

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A028554

Palindromes of form n(n+3).

+10
3

0, 4, 88, 868, 4554, 8008, 45154, 89698, 452254, 4526254, 8996998, 830333038, 862626268, 899969998, 4058008504, 45032023054, 45229592254, 89999699998, 405485584504, 4503764673054, 8187727277818, 8999996999998, 89178266287198, 455467838764554, 833066101660338

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Also: Palindromes that are the sum of consecutive initial even composites. Sequence 4 + 6 + 8 + 10 + 12 + 14 + ... + z = n. For values of z see A058851. (Comment added by author 12/2000).

9*10^(2n)-3*10^n-2 for n >= 0 are terms. For n > 1, the first (and last digit) of a(n) is either 4 or 8. - Chai Wah Wu, Feb 20 2021

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..40

P. De Geest, Palindromic Quasipronics

P. De Geest, Palindromic Sums 2

PROG

(Python)

n, m, A028554_list = 4, 0, []

while n < 10**12:

s = str(m)

if s == s[::-1]:

A028554_list.append(m)

m += n

n += 2 # Chai Wah Wu, Feb 20 2021

CROSSREFS

Cf. A028553, A058851.

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

EXTENSIONS

More terms from Chai Wah Wu, Feb 20 2021

STATUS

approved

A058851

Sum of even composites up to n is palindromic.

+10
3

4, 18, 58, 134, 178, 424, 598, 1344, 4254, 5998, 57630, 58740, 59998, 127404, 424414, 425344, 599998, 1273554, 4244414, 5722840, 5999998, 18886848, 42683384, 57725768, 59999998, 424650414, 578107368, 588254658, 588349340

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Sequence is 4 + 6 + 8 + 10 + 12 + 14 + ... + n.

6*10^n-2 for n >=0 are terms. - Chai Wah Wu, Feb 20 2021

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..40

P. De Geest, Palindromic Sums

FORMULA

a(n) = 2*(1+A028553(1+n)). - R. J. Mathar, Sep 09 2015