A288519 a(n) = least k such that A080670(k) begins with n.

1, 2, 3, 41, 5, 61, 7, 83, 97, 101, 11, 127, 13, 149, 151, 163, 17, 181, 19, 2003, 22, 4, 6, 16, 10, 64, 14, 166, 29, 307, 31, 9, 27, 81, 15, 183, 21, 249, 291, 401, 41, 421, 43, 443, 457, 461, 47, 487, 491, 503, 55, 25, 53, 205, 265, 305, 35, 415, 59, 601, 61

Offset

1,2

Comments

a(p) <= p for any prime p.

a(n) <= A018800(n) for any n > 0.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Scatterplot of the first 1000000 terms

Rémy Sigrist, PARI program for A288519

Example

The following table shows the first values from A080670, as well as the terms that can be derived from it:
k       A080670(k)      Derived terms
--      ----------      -------------
1       1               a(1) = 1
2       2               a(2) = 2
3       3               a(3) = 3
4       22              a(22) = 4
5       5               a(5) = 5
6       23              a(23) = 6
7       7               a(7) = 7
8       23              none
9       32              a(32) = 9
10      25              a(25) = 10
11      11              a(11) = 11
12      223             a(223) = 12
13      13              a(13) = 13
14      27              a(27) = 14
15      35              a(35) = 15
16      24              a(24) = 16
17      17              a(17) = 17
18      232             a(232) = 18
19      19              a(19) = 19
20      225             a(225) = 20
21      37              a(37) = 21
22      211             a(211) = 22, a(21) = 22
23      23              none
24      233             a(233) = 24
25      52              a(52) = 25

Mathematica

s = Array[Flatten@ Map[IntegerDigits, DeleteCases[ Flatten@ FactorInteger@ #, 1] /. {} -> {1}] &, 10^4]; FromDigits /@ Table[ Function[k, SelectFirst[s, If[Length@# > 0, #[[1, 1]] == 1, False] &@ SequencePosition[#, k] &]]@ IntegerDigits[n], {n, 61}] (* Michael De Vlieger, Jun 11 2017 *)

Crossrefs

Cf. A018800, A080670.

Sequence in context: A077336 A242174 A340394 * A240588 A013646 A059800

Adjacent sequences: A288516 A288517 A288518 * A288520 A288521 A288522

Keyword

nonn,base,look

Author

Rémy Sigrist, Jun 10 2017

Status

approved