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 A050782 Smallest positive multiplier m such that m*n is palindromic (or zero if no such m exists). 19
 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 21, 38, 18, 35, 17, 16, 14, 9, 0, 12, 1, 7, 29, 21, 19, 37, 9, 8, 0, 14, 66, 1, 8, 15, 7, 3, 13, 15, 0, 16, 6, 23, 1, 13, 9, 3, 44, 7, 0, 19, 13, 4, 518, 1, 11, 3, 4, 13, 0, 442, 7, 4, 33, 9, 1, 11, 4, 6, 0, 845, 88, 4, 3, 7, 287, 1, 11, 6, 0, 12345679, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Multiples of 81 require the largest multipliers. From Jon E. Schoenfield, Jan 15 2015: (Start) In general, a(n) is large when n is a multiple of 81. E.g., for n in [1..10000], of the 9000 terms where a(n)>0, 111 are at indices n that are multiples of 81; of the remaining 8889 terms, 755 are in [1..9], 1760 are in [10..99], 3439 are in [100..999], 2180 are in [1000..9999], 708 are in [10000..99999], 36 are in [100000..999999], 6 are in [1000000..9999999], 2 are in [10000000..99999999], 2 are in [100000000..999999999], and 1 (the largest) is a(8891) = 8546948927, but the smallest of the 111 terms whose indices are multiples of 81 is a(2997)=333667. (End) a(n) = 0 iff 10 | n. a(n) = 1 iff n is a palindrome. If k | a(n) then a(k*n) = a(n)/k. - Robert Israel, Jan 15 2015 LINKS Giovanni Resta, Table of n, a(n) for n = 0..10000 (first 8181 terms from Chai Wah Wu) Patrick De Geest, World!Of Numbers EXAMPLE E.g., a(81) -> 81 * 12345679 = 999999999 and a palindrome. MAPLE digrev:= proc(n) local L, d, i; L:= convert(n, base, 10); d:= nops(L); add(L[i]*10^(d-i), i=1..d); end proc: f:= proc(n) local d, d2, x, t, y; if n mod 10 = 0 then return 0 fi; if n < 10 then return 1 fi; for d from 2 do if d::even then d2:= d/2; for x from 10^(d2-1) to 10^d2-1 do t:= x*10^d2 + digrev(x); if t mod n = 0 then return(t/n) fi; od else d2:= (d-1)/2; for x from 10^(d2-1) to 10^d2-1 do for y from 0 to 9 do t:= x*10^(d2+1)+y*10^d2+digrev(x); if t mod n = 0 then return(t/n) fi; od od fi od; end proc: seq(f(n), n=0 .. 100); # Robert Israel, Jan 15 2015 MATHEMATICA t={0}; Do[i=1; If[IntegerQ[n/10], y=0, While[Reverse[x=IntegerDigits[i*n]]!=x, i++]; y=i]; AppendTo[t, y], {n, 80}]; t (* Jayanta Basu, Jun 01 2013 *) PROG (Python) from __future__ import division def palgen(l, b=10): # generator of palindromes in base b of length <= 2*l if l > 0: yield 0 for x in range(1, l+1): n = b**(x-1) n2 = n*b for y in range(n, n2): k, m = y//b, 0 while k >= b: k, r = divmod(k, b) m = b*m + r yield y*n + b*m + k for y in range(n, n2): k, m = y, 0 while k >= b: k, r = divmod(k, b) m = b*m + r yield y*n2 + b*m + k def A050782(n, l=10): if n % 10: x = palgen(l) next(x) # replace with x.next() in Python 2.x for i in x: q, r = divmod(i, n) if not r: return q else: return 'search limit reached.' else: return 0 # Chai Wah Wu, Dec 30 2014 CROSSREFS Cf. A002113, A020485, A050810. Sequence in context: A083567 A109211 A224701 * A061906 A139768 A307278 Adjacent sequences: A050779 A050780 A050781 * A050783 A050784 A050785 KEYWORD nonn,base,nice AUTHOR Patrick De Geest, Oct 15 1999 STATUS approved

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Last modified February 26 13:41 EST 2024. Contains 370352 sequences. (Running on oeis4.)