A357045 Lexicographically earliest sequence of distinct non-palindromic numbers (A029742) such that a(n)+a(n+1) is always a palindrome (A002113).

10, 12, 21, 23, 32, 34, 43, 45, 54, 47, 19, 14, 30, 25, 41, 36, 52, 49, 17, 16, 28, 27, 39, 38, 50, 51, 15, 18, 26, 29, 37, 40, 48, 53, 13, 20, 24, 31, 35, 42, 46, 65, 56, 75, 76, 85, 86, 95, 96, 106, 116, 126, 136, 146, 157, 105, 97, 64, 57, 74

Offset

1,1

Comments

Conjecture: The sequence contains all non-palindromic numbers (A029742).

Links

Table of n, a(n) for n=1..60.

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

Prog

(PARI) A357045_first(n, U=[9], a=1)={vector(n, k, k=U[1]; until( is_A002113(a+k) && !is_A002113(k) && !setsearch(U, k), k++); U=setunion(U, [a=k]); while(#U>1 && U[2]==U[1]+1+is_A002113(U[1]+1), U=U[^1]); a)}
(Python)
from itertools import count, islice
def ispal(n): s = str(n); return s == s[::-1]
def agen():
    aset, k, mink = {10}, 10, 12
    while True:
        an = k; yield an; aset.add(an); k = mink
        while k in aset or ispal(k) or not ispal(an+k): k += 1
        while mink in aset: mink += 1
print(list(islice(agen(), 60))) # Michael S. Branicky, Sep 14 2022

Crossrefs

Cf. A029742 (non-palindromes), A002113 (palindromes), A357044 (palindromes with non-palindromic sum of neighbors).

Sequence in context: A215940 A368550 A337866 * A320170 A082927 A108965

Adjacent sequences: A357042 A357043 A357044 * A357046 A357047 A357048

Keyword

nonn,base

Author

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

Status

approved