1. Sum of the first n primes is palindromic.
Sequence = 2 + 3 + 5 + 7 + 11 + 13 + ... + z Index entries in OEIS A038582, A038584 and A038583 Other sources : Puzzle 7
2. Sum of the first n odd primes is palindromic.
Sequence = 3 + 5 + 7 + 11 + 13 + 17 + ... + z Index entries in OEIS A058845, A058846 and A058847
3. Sum of the first n composites is palindromic.
Sequence = 4 + 6 + 8 + 9 + 10 + 12 + ... + z Index entries in OEIS A053779, A057959 and A053780 Other sources : Puzzle 89
4. Sum of the first n odd composites is palindromic.
Sequence = 9 + 15 + 21 + 25 + 27 + 33 + ... + z Index entries in OEIS A058848, A058849 and A058850 Other sources : Puzzle 89
5. Sum of the first n even composites is palindromic.
Sequence = 4 + 6 + 8 + 10 + 12 + 14 + ... + z Index entries in OEIS A028553, A058851 and A028554 Aldo Palindromic numbers of the form n(n+3). Main source see Palindromes of the form n(n+3) The following substitution shows why the sequence equals x * (x + 3) The sequence can be rewritten as 2 * (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ...) The second term is 'the sum of the natural numbers' minus the starting number 1. Replace it with the general formula we get 2 * [ (n^2 + n)/2 1 ] or [ n^2 + n 2 ] Substitute n with (x + 1) we get [ (x + 1)^2 + (x + 1) 2 ] and work it out. The sequence evolves from [ x^2 + 2x + 1 + x + 1 2 ] to [ x^2 + 3x ] which finally yields to x * (x + 3) QED
Aldo Palindromic numbers of the form n(n+3). Main source see Palindromes of the form n(n+3)
The sequence can be rewritten as 2 * (2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + ...) The second term is 'the sum of the natural numbers' minus the starting number 1. Replace it with the general formula we get 2 * [ (n^2 + n)/2 1 ] or [ n^2 + n 2 ] Substitute n with (x + 1) we get [ (x + 1)^2 + (x + 1) 2 ] and work it out. The sequence evolves from [ x^2 + 2x + 1 + x + 1 2 ] to [ x^2 + 3x ] which finally yields to x * (x + 3) QED
6. Sum of the first n palindromes is palindromic.
Sequence = 1 + 2 + 3 + 4 + 5 + 6 + ... + z Index entries in OEIS A046486 and A046487
7. Sum of the first n numbers is palindromic.
Sequence = 1 + 2 + 3 + 4 + 5 + 6 + ... + z Main source see Palindromic Triangulars
8. Sum of the first n odd numbers is palindromic.
Sequence = 1 + 3 + 5 + 7 + 9 + 11 + ... + z Main source see Palindromic Squares
9. Sum of the first n even numbers is palindromic.
Sequence = 2 + 4 + 6 + 8 + 10 + 12 + ... + z Main source see Palindromic Pronic Numbers
Enoch Haga (email) from California, USA.
Jeff Heleen (email) from New Hampshire, USA.
G. L. Honaker, Jr. (email) from Bristol, Virginia, USA.
Jud McCranie (email) from USA.
Carlos Rivera (email) from Monterrey, Nuevo León, México.
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