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

Author

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

Keywords

• nonn
• base

Comments

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

Links

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

Crossrefs

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

Programs

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