

A210538


Least integer not occurring earlier, divisible by the nth digit (or 10 for digit '0') of the sequence.


2



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 12, 30, 11, 14, 15, 40, 13, 16, 17, 24, 18, 25, 28, 50, 19, 21, 22, 36, 23, 35, 26, 32, 27, 48, 34, 45, 38, 56, 55, 60, 29, 54, 42, 31, 44, 46, 33, 66, 52, 39, 51, 65, 58, 72, 57, 62, 64, 49, 68, 80, 63, 76, 84, 70, 69, 88, 75, 78, 85, 90, 96, 100, 74, 81
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OFFSET

1,2


COMMENTS

The first 10 terms are justified "a posteriori", i.e., they add the digit used in their own check for divisibility. Note that the title and definition (but not example) in Angelini's original post (cf. link) corresponds to a much more involved selfreferencing sequence.
Primes > 7 occur at indices corresponding to digits "1" of the concatenated terms, e.g. 11=a(14), and the 14th digit is the "1" in a(12)=12. The reciprocal is not true, e.g., the 10th, 19th, 22nd, 28th and 34th digits are "1" but for these n, a(n) is composite. The next counterexample is n=187, the last of 5 consecutive indices of "1"s. See A210539 for the list of these counterexamples and more details.


LINKS

M. F. Hasler, Table of n, a(n) for n = 1..3702
E. Angelini, a(n) is divisible by the a(n)th digit of S, SeqFan list, Mar 22 2012


EXAMPLE

Cf. link.


PROG

(PARI) {S=[u=0]; while(#S<99, for(a=1, 9e9, bittest(u, a)&next; a>9 & a%if(S[1], S[1], 10) & next; print1(a", "); u+=1<<a; a>10 &
S=concat(vecextract(S, "^1"), eval(Vec(Str( a )))); break))}


CROSSREFS

Sequence in context: A108193 A089583 A264979 * A247143 A257128 A247808
Adjacent sequences: A210535 A210536 A210537 * A210539 A210540 A210541


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, following the idea of Eric Angelini, Mar 22 2012


STATUS

approved



