A289469 Numbers k such that it is possible to form a palindrome by concatenating the first k positive integers in some order.

1, 19, 20, 21, 22, 39, 40, 41, 59, 60, 61, 79, 80, 81, 98, 99, 122, 201, 219, 220

Offset

1,2

Comments

For k=19 and k=20 there are 8! such palindromes.

There are no such palindromes for k = 101, 119, 121, 139, 141, 159, 161, 179, 181, 199. This is because it is impossible to have a pair matching "100".

It is unknown whether there exist palindromes that are a concatenation of the first k primes. The list of k for which such palindromes could exist is in S001070 (see Noe's link). It has been proven that k=36 and k=247 cannot exist.

For k=21, 11612160 admissible permutations produce 8069040 distinct palindromes. These counts are respectively equal to 20240640 and 13633200 for k=22. - Giovanni Resta, Sep 02 2017

Links

Table of n, a(n) for n=1..20.

Tony D. Noe, S001070

Tony D. Noe, S001071

Carlos Rivera, Puzzle 891: The first N integers arranged to form a Palindrome, The Prime Puzzles and Problems Connection.

Example

For k=19 one palindrome is 1.12.3.14.7.15.6.18.9.10.19.8.16.5.17.4.13.2.11 => 11231471561891019816517413211. This palindrome is the smallest such palindrome that is prime.

Crossrefs

Cf. A291633.

Sequence in context: A103418 A004508 A018824 * A093680 A007640 A265201

Adjacent sequences: A289466 A289467 A289468 * A289470 A289471 A289472

Keyword

nonn,base,hard,more

Author

Dmitry Kamenetsky, Sep 02 2017

Status

approved