A357044 Lexicographic earliest sequence of distinct palindromes (A002113) such that a(n)+a(n+1) is never palindromic.

1, 9, 3, 7, 5, 8, 2, 11, 4, 6, 22, 88, 44, 66, 77, 33, 99, 55, 101, 909, 111, 191, 121, 181, 131, 171, 141, 161, 151, 252, 262, 242, 272, 232, 282, 222, 292, 212, 393, 313, 494, 323, 383, 333, 373, 343, 363, 353, 454, 464, 444, 474, 434, 484, 424

Offset

1,2

Comments

Obviously the sequence cannot contain 0.

It is easy to prove that the sequence is a permutation of the nonzero palindromes (in the sense that it contains each of them exactly once).

Links

Table of n, a(n) for n=1..55.

Eric Angelini, Sums with palindromes, personal blog "Cinquante signes" on blogspot.com, and post to the math-fun list, Sep 12 2022

Prog

(PARI) A357044_first(n, U=[0], a=9)={vector(n, k, k=U[1]; while(is_A002113(a+k=A262038(k+1)) || setsearch(U, k), ); U=setunion(U, [a=k]); while(#U>1 && U[2]==A262038(U[1]+1), U=U[^1]); a)}
(Python)
from itertools import count, islice
def ispal(n): s = str(n); return s == s[::-1]
def nextpal(p): # next largest palindrome after palindrome p
    d = str(p)
    if set(d) == {'9'}: return int('1' + '0'*(len(d)-1) + '1')
    h = str(int(d[:(len(d)+1)//2]) + 1)
    return int(h + h[:-1][::-1]) if len(d)&1 else int(h + h[::-1])
def agen():
    aset, pal, minpal = {1}, 1, 2
    while True:
        an = pal; yield an; aset.add(an); pal = minpal
        while pal in aset or ispal(an+pal): pal = nextpal(pal)
        while minpal in aset: minpal = nextpal(minpal)
print(list(islice(agen(), 55))) # Michael S. Branicky, Sep 14 2022

Crossrefs

Cf. A002113 (palindromes), A029742 (non-palindromes), A262038 (next palindrome), A357045 (non-palindromes with palindromic sum of neighbors).

Sequence in context: A346989 A136251 A073002 * A348302 A197836 A011282

Adjacent sequences: A357041 A357042 A357043 * A357045 A357046 A357047

Keyword

nonn,base

Author

Eric Angelini and M. F. Hasler, Sep 14 2022

Status

approved