A210538 Least integer not occurring earlier, divisible by the n-th digit (or 10 for digit '0') of the sequence.

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

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 self-referencing 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 converse 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

Eric 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: A319726 A302589 A375755 * A247143 A257128 A339541

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