A114319 - OEIS

%I #51 Nov 25 2023 08:42:10

%S 1,2,3,5,7,4,10,8,11,12,13,14,15,16,18,19,20,22,24,26,27,28,29,30,32,

%T 34,35,36,38,40,41,42,43,44,46,47,48,50,53,55,57,59,65,68,69,70,71,72,

%U 73,74,75,76,79,84,85,86,87,88,89,90,91,92,94,95,96,98,103,107

%N Lexicographically earliest sequence of positive distinct terms such that the a(n)th digit of the sequence is noncomposite (see the Comments section).

%C "Noncomposite" digits are 0, 1, 2, 3, 5 and 7.

%H David Consiglio, Jr., <a href="/A114319/b114319.txt">Table of n, a(n) for n = 1..1000</a>

%e Noncomposite digits are between parentheses:

%e Sequence: 1,2,3,5,7,4,10,8,11,12,...

%e Sequence: (1),(2),(3),(5),(7),4,(1)(0),8,(1)(1),(1)(2),...

%e Digit position: 1st, 2nd, 3rd, 4th, 5th, 7th, 8th, 10th, 11th, 12th, ... = a reordering of the sequence itself.

%o (Python)

%o noncomp = [0, 1, 2, 3, 5, 7]

%o terms = [1, 2, 3, 5, 7, 4, 10, 8]

%o def si(test_list):  # all terms greater than 0 and no repetitions

%o     a = all(i > 0 for i in test_list)

%o     b = len(test_list) == len(set(test_list))

%o     return a & b

%o def clear(test_list):  # sequence meets definitional criteria

%o     full = "".join(str(x) for x in test_list)

%o     for a in test_list:

%o         if int(a) - 1 >= len(full):

%o             return True

%o         elif int(full[int(a) - 1]) not in noncomp:

%o             return False

%o     return True

%o while len(terms) < 100:

%o     start = 1

%o     while True:

%o         terms.append(start)

%o         if si(terms) and clear(terms):

%o             break

%o         else:

%o             terms.pop()

%o             start += 1

%o print(terms)

%o # _David Consiglio, Jr._, Oct 30 2023

%Y Cf. A114316 (same idea but with "nonprime" digits 0, 1, 4, 6, 8 and 9).

%K nonn,base,easy

%O 1,2

%A _Eric Angelini_, Feb 05 2006

%E Corrected by the author on Feb 24 2020 thanks to _R. J. Mathar_ and _Bernard Schott_