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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 (list; graph; refs; listen; history; text; internal format)
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

Colin Barker, Table of n, a(n) for n = 1..1000

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: A095046 A166667 A121458 * A254330 A052260 A067833

Adjacent sequences:  A268485 A268486 A268487 * A268489 A268490 A268491

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Feb 14 2016

STATUS

approved

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Last modified May 30 11:18 EDT 2020. Contains 334724 sequences. (Running on oeis4.)