This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Select[Range@ 101, MemberQ[IntegerDigits[#, MixedRadix[Reverse@ Range@ 12]], 1] &] (* Michael De Vlieger, May 30 2016, Version 10.2 *) r = MixedRadix[Reverse@ Range[2, 12]]; Select[Range@ 101, Min[IntegerDigits[#, r] /. 0 -> Nothing] == 1 &] (* Michael De Vlieger, Aug 14 2016, Version 10.2 *)
def A(n, p=2): return n if n=1]) # Indranil Ghosh, Jun 19 2017
To recover n from a(n) the digits in positions i = 1, 2, 3, ... (starting indexing from the least significant digit at right) are multiplied by A001563(i) and added together: ---------------- n a(n) ---------------- 0 0 1 1 2 2 3 3 4 10 5 11 6 12 7 13 8 20 9 21 10 22 11 23 12 30 13 31 14 32 15 33 16 40 17 41 (as 4*A001563(2) + 1*A001563(1) = 17) 18 100 (as 1*A001563(3) + 0*A001563(2) + 0*A001563(1) = 18) and: 3225599 99111111 (as 3225599 = 9*b(8) + 9*b(7) + b(6) + b(5) + b(4) + b(3) + b(2) + b(1)), where b(n) = A001563(n).
f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@ NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; Table[FromDigits@ f@ n, {n, 72}] (* Michael De Vlieger, Aug 31 2016 *)
(define (A276326 n) (let loop ((n n) (s 0)) (if (zero? n) s (let ((dig (A276333 n))) (if (> dig 9) (error "A276326: ambiguous representation of n, digit > 9 would be needed: " n dig) (loop (A276335 n) (+ s (* dig (expt 10 (- (A258198 n) 1))))))))))
Table[# #! &@ NestWhile[# + 1 &, 0, # #! <= n &[# + 1] &], {n, 0, 96}] (* Michael De Vlieger, Aug 31 2016 *)
For n=1, the largest term of A001563 <= 1 is A001563(1) = 1, thus a(1) = 1. For n=2, the largest term of A001563 <= 2 is A001563(1) = 1, thus a(2) = 1 + a(2-1) = 2. For n=18, the largest term of A001563 <= 18 is A001563(3) = 18, thus a(18) = 1. For n=20, the largest term of A001563 <= 20 is A001563(3) = 18, thus a(20) = 1 + a(20-18) = 3. For n=36, the largest term of A001563 <= 36 is A001563(3) = 18, thus a(36) = 1 + a(18) = 2.
f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; {0}~Join~Table[Total@ f@ n, {n, 120}] (* Michael De Vlieger, Aug 31 2016 *)
f[n_] := Block[{a = {{0, n}}}, Do[AppendTo[a, {First@ #, Last@ #} &@ QuotientRemainder[a[[-1, -1]], (# #!) &[# - i]]], {i, 0, # - 1}] &@ NestWhile[# + 1 &, 0, (# #!) &[# + 1] <= n &]; Rest[a][[All, 1]]]; Table[Length@ TakeWhile[Reverse@ f@ n, # == 0 &] + 1, {n, 120}] (* Michael De Vlieger, Aug 31 2016 *)
(define (A276329 n) (let loop ((i (A258198 n))) (cond ((zero? i) 1) ((zero? (modulo n (A001563 i))) i) (else (loop (- i 1))))))
Comments