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A268488
Least number k of the form k = n*(k % 10) + [k / 10], where k % 10 = last digit of k, [k / 10] = k without its last digit.
3
1, 19, 29, 13, 49, 59, 23, 79, 89, 11, 109, 119, 43, 139, 149, 53, 169, 179, 21, 199, 209, 73, 229, 239, 83, 259, 269, 31, 289, 299, 103, 319, 329, 113, 349, 359, 41, 379, 389, 133, 409, 419, 143, 439, 449, 51, 469, 479, 163, 499, 509, 173, 529, 539, 61
OFFSET
1,2
COMMENTS
E. Angelini considered 3, 29, 289, 321, ... obtained by iteration of this map, while the lexicographic first nontrivial sequence obtained that way is 2, 19, 21, 209, 2089, 2321, 23209, 77363, 773629, ... See A268492, A268493 for these two sequences.
LINKS
Eric Angelini (and reply by M. Hasler), 3, 29, 289, 321, ..., SeqFan list, Feb. 13, 2016
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: x*(1 +19*x +29*x^2 +13*x^3 +49*x^4 +59*x^5 +23*x^6 +79*x^7 +89*x^8 +9*x^9 +71*x^10 +61*x^11 +17*x^12 +41*x^13 +31*x^14 +7*x^15 +11*x^16 +x^17) / ((1 -x)^2*(1 +x +x^2)^2*(1 +x^3 +x^6)^2). - Colin Barker, Feb 15 2016 and Feb 22 2016
a(n) = 2*a(n-9)-a(n-18) for n>18. - Colin Barker, Feb 15 2016
a(n) = if n mod 9 == 1 then (n-1)/9*10+1 else if n mod 3 == 1 then (n-1)/3*10+3 else n*10-1, cf. SeqFan post for the proof. This implies the above recurrence relation and generating function. - M. F. Hasler, Feb 15 2016
MATHEMATICA
Table[SelectFirst[Range@ 1000, # == n Mod[#, 10] + Floor[#/10] &], {n,
55}] (* Version 10, or *)
Table[k = 1; While[k != n Mod[k, 10] + Floor[k/10], k++]; k, {n, 55}] (* Michael De Vlieger, Feb 15 2016 *)
PROG
(PARI) A268488(n)=if(n%9==1, n\9*10+1, if(n%3==1, n\3*10+3, n*10-1))
(PARI) a(n) = k=1; while(k != n*(k%10)+k\10, k++); k
vector(100, n, a(n)) \\ Colin Barker, Feb 15 2016
(PARI) Vec(x*(1 +19*x +29*x^2 +13*x^3 +49*x^4 +59*x^5 +23*x^6 +79*x^7 +89*x^8 +9*x^9 +71*x^10 +61*x^11 +17*x^12 +41*x^13 +31*x^14 +7*x^15 +11*x^16 +x^17) / ((1 -x)^2*(1 +x +x^2)^2*(1 +x^3 +x^6)^2) + O(x^40)) \\ Colin Barker, Feb 22 2016
CROSSREFS
Cf. A268492 and A268493 for the orbits of 2 and 3 under this map.
Sequence in context: A166667 A121458 A373859 * A254330 A052260 A067833
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 14 2016
STATUS
approved