A114319 Lexicographically earliest sequence of positive distinct terms such that the a(n)th digit of the sequence is noncomposite (see the Comments section).

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, 34, 35, 36, 38, 40, 41, 42, 43, 44, 46, 47, 48, 50, 53, 55, 57, 59, 65, 68, 69, 70, 71, 72, 73, 74, 75, 76, 79, 84, 85, 86, 87, 88, 89, 90, 91, 92, 94, 95, 96, 98, 103, 107

Offset

1,2

Comments

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

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..1000

Example

Noncomposite digits are between parentheses:
Sequence: 1,2,3,5,7,4,10,8,11,12,...
Sequence: (1),(2),(3),(5),(7),4,(1)(0),8,(1)(1),(1)(2),...
Digit position: 1st, 2nd, 3rd, 4th, 5th, 7th, 8th, 10th, 11th, 12th, ... = a reordering of the sequence itself.

Prog

(Python)
noncomp = [0, 1, 2, 3, 5, 7]
terms = [1, 2, 3, 5, 7, 4, 10, 8]
def si(test_list):  # all terms greater than 0 and no repetitions
    a = all(i > 0 for i in test_list)
    b = len(test_list) == len(set(test_list))
    return a & b
def clear(test_list):  # sequence meets definitional criteria
    full = "".join(str(x) for x in test_list)
    for a in test_list:
        if int(a) - 1 >= len(full):
            return True
        elif int(full[int(a) - 1]) not in noncomp:
            return False
    return True
while len(terms) < 100:
    start = 1
    while True:
        terms.append(start)
        if si(terms) and clear(terms):
            break
        else:
            terms.pop()
            start += 1
print(terms)
# David Consiglio, Jr., Oct 30 2023

Crossrefs

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

Sequence in context: A284145 A284189 A373999 * A125151 A372130 A302024

Adjacent sequences: A114316 A114317 A114318 * A114320 A114321 A114322

Keyword

nonn,base,easy

Author

Eric Angelini, Feb 05 2006

Extensions

Corrected by the author on Feb 24 2020 thanks to R. J. Mathar and Bernard Schott

Status

approved