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
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
Programs
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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)}
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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
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