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A301382
a(1) = 1. For n > 1, a(n) is the smallest positive integer x not already in the sequence such that the product of x and its initial digit is minimal and strictly larger than the same product for any previous term.
2
1, 2, 3, 10, 11, 12, 13, 14, 15, 4, 17, 18, 19, 5, 6, 20, 21, 22, 23, 24, 7, 25, 26, 27, 28, 29, 8, 9, 30, 31, 32, 33, 100, 101, 34, 103, 104, 35, 106, 107, 36, 109, 110, 37, 112, 113, 38, 115, 116, 39, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136
OFFSET
1,2
COMMENTS
We see in the Example section that P is the smallest possible product strictly bigger than the previous one and not leading to a contradiction.
LINKS
EXAMPLE
a(1) * [the first digit of a(1)] = 1 * 1 = P = 1
a(2) * [the first digit of a(2)] = 2 * 2 = P = 4
a(3) * [the first digit of a(3)] = 3 * 3 = P = 9
a(4) * [the first digit of a(4)] = 10 * 1 = P = 10
a(5) * [the first digit of a(5)] = 11 * 1 = P = 11
a(6) * [the first digit of a(6)] = 12 * 1 = P = 12
a(7) * [the first digit of a(7)] = 13 * 1 = P = 13
a(8) * [the first digit of a(8)] = 14 * 1 = P = 14
a(9) * [the first digit of a(9)] = 15 * 1 = P = 15
a(10) * [the first digit of a(10)] = 4 * 4 = P = 16
a(11) * [the first digit of a(11)] = 17 * 1 = P = 17
Etc.
PROG
(PARI) p = vector(136, k, oo); for (n=1, #p, x = n*digits(n)[1]; if (x<=#p, p[x] = min(p[x], n))); for (k=1, #p, if (p[k] != oo, print1 (p[k] ", "))) \\ Rémy Sigrist, Mar 22 2018
CROSSREFS
Sequence in context: A283436 A225558 A362089 * A288657 A055655 A371030
KEYWORD
nonn,base
AUTHOR
STATUS
approved