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 A319586 Number of n-digit base-10 palindromes (A002113) that cannot be written as the sum of two positive base-10 palindromes. 1
 2, 0, 8, 7, 95, 94, 975, 971, 9810, 9805, 98288, 98272 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..12. EXAMPLE a(1) = 2, because 0 and 1 are not sums of two positive 1-digit integers, all of which are palindromes. a(3) = 8, because the 8 3-digit palindromes 111, 131, 141, 151, 161, 171, 181, and 191 (A213879(2) ... A213879(9)) cannot be written as sum of two nonzero palindromes. PROG (PARI) \\ calculates a(2)...a(8) using M. F. Hasler's functions in A002113 A002113(n)={my(L=logint(n, 10)); (n-=L=10^max(L-(n<11*10^(L-1)), 0))*L+fromdigits(Vecrev(digits(if(nP/2, break); if(is_A002113(P-PP), issum=1; break)); if(issum==0, j++)); print1(j, ", ", )) (Python) from sympy import isprime from itertools import product def pals(d, base=10): # all d-digit palindromes digits = "".join(str(i) for i in range(base)) for p in product(digits, repeat=d//2): if d > 1 and p[0] == "0": continue left = "".join(p); right = left[::-1] for mid in [[""], digits][d%2]: yield int(left + mid + right) def a(n): palslst = [p for d in range(1, n+1) for p in pals(d)][1:] palsset = set(palslst) cs = ctot = 0 for p in pals(n): ctot += 1 for p1 in palslst: if p - p1 in palsset: cs += 1; break if p1 > p//2: break return ctot - cs print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Jul 12 2021 CROSSREFS Cf. A002113, A035137, A213879, A319477. Sequence in context: A366164 A021483 A011015 * A287467 A288015 A288438 Adjacent sequences: A319583 A319584 A319585 * A319587 A319588 A319589 KEYWORD nonn,base,hard,more AUTHOR Hugo Pfoertner, Sep 23 2018 EXTENSIONS a(12) from Giovanni Resta, Oct 01 2018 STATUS approved

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Last modified May 24 05:24 EDT 2024. Contains 372772 sequences. (Running on oeis4.)