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 A342356 a(1) = 1, a(2) = 10; for n > 2, a(n) is the least positive integer not occurring earlier that shares both a factor and a digit with a(n-1). 3
 1, 10, 12, 2, 20, 22, 24, 4, 14, 16, 6, 26, 28, 8, 18, 15, 5, 25, 35, 30, 3, 33, 36, 32, 34, 38, 48, 40, 42, 21, 27, 57, 45, 50, 52, 54, 44, 46, 56, 58, 68, 60, 62, 64, 66, 63, 39, 9, 69, 90, 70, 7, 77, 147, 49, 84, 74, 37, 333, 93, 31, 124, 72, 75, 51, 17, 102, 80, 78, 76, 86, 82, 88, 98, 91 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS After 100000 terms the lowest unused number is 18181. The sequence is likely a permutation of the positive integers. LINKS Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n. MATHEMATICA Block[{a = {1, 10}, m = {1, 0}, k}, Do[k = 2; While[Nand[FreeQ[a, k], GCD[k, a[[-1]]] > 1, IntersectingQ[m, IntegerDigits[k]]], k++]; AppendTo[a, k]; Set[m, IntegerDigits[k]], {i, 73}]; a] (* Michael De Vlieger, Mar 11 2021 *) PROG (Python) from sympy import factorint def aupton(terms):   alst, aset = [1, 10], {1, 10}   for n in range(3, terms+1):     an = 1     anm1_digs, anm1_factors = set(str(alst[-1])), set(factorint(alst[-1]))     while True:       while an in aset: an += 1       if set(str(an)) & anm1_digs != set():         if set(factorint(an)) & anm1_factors != set():           alst.append(an); aset.add(an); break       an += 1   return alst print(aupton(75)) # Michael S. Branicky, Mar 09 2021 CROSSREFS Cf. A342366 (share factor but not digit), A239664 (no shared factor or digit), A342367 (share digit but not factor), A184992, A309151, A249591. Sequence in context: A278856 A316914 A350444 * A338290 A284229 A078285 Adjacent sequences:  A342353 A342354 A342355 * A342357 A342358 A342359 KEYWORD nonn,base AUTHOR Scott R. Shannon, Mar 08 2021 STATUS approved

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Last modified August 18 19:12 EDT 2022. Contains 356215 sequences. (Running on oeis4.)