A329545 After a(1) = 1, add the even terms and subtract the odd ones, the result must always be a palindrome. This is the lexicographically earliest sequence of distinct positive integers with this property.

1, 2, 3, 4, 18, 11, 5, 16, 13, 7, 6, 14, 15, 26, 22, 33, 17, 28, 25, 36, 35, 9, 8, 58, 55, 44, 46, 10, 20, 30, 73, 77, 66, 24, 40, 50, 103, 79, 68, 34, 23, 81, 48, 47, 80, 83, 72, 54, 43, 85, 52, 49, 38, 37, 70, 64, 53, 87, 32, 27, 60, 57, 90, 12, 45, 59, 92, 42, 75, 61, 94, 62, 95, 63, 74, 69, 194

Offset

1,2

Comments

Negative palindromes are not allowed. After 50000 terms, the smallest unused integers are 964, 1020, 1029, 1031, 1038, 1041, 1047, 1051, ... and the largest used is 173410. The largest palindrome produced so far is 309903. Is the sequence a permutation of the integers > 0?

a(63411) = 964. Rémy Sigrist's comment in A329544 shows that terms in A104444 are not in the sequence. Conjecture: Sequence is a permutation of positive integers not in A104444. - Chai Wah Wu, Dec 11 2019

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..49999

Example

The sequence starts with 1, smallest positive integer.
1 + 2 = 3 (palindrome)
1 + 2 - 3 = 0 (palindrome)
1 + 2 - 3 + 4 = 1 (palindrome)
1 + 2 - 3 + 4 + 18 = 22 (palindrome)
1 + 2 - 3 + 4 + 18 - 11 = 11 (palindrome)
1 + 2 - 3 + 4 + 18 - 11 - 5 = 6 (palindrome)
1 + 2 - 3 + 4 + 18 - 11 - 5 + 16 = 22 (palindrome), etc.

Prog

(PARI) A329545_vec(N, u=1, U, a, s=2, d)={vector(N, n, a=u; while(bittest(U, a-u)|| Vecrev(d=digits(s+(-1)^a*a))!=d|| (a>s&&bittest(a, 0)), a++); s+=(-1)^a*a; U+=1<<(a-u); while(bittest(U, 0), U>>=1; u++); a)} \\ M. F. Hasler, Nov 16 2019

Crossrefs

Cf. A329544 (same idea, but where the odd integers are added and the even ones are subtracted).

Cf. A002113 (palindromes), A086862 (first differences of palindromes).

Cf. A104444.

Sequence in context: A037430 A377958 A370868 * A187075 A154715 A077407

Adjacent sequences: A329542 A329543 A329544 * A329546 A329547 A329548

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Nov 16 2019

Status

approved