A357045 - OEIS

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

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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).