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

%I A288519 #9 Jun 12 2017 00:46:24
%S A288519 1,2,3,41,5,61,7,83,97,101,11,127,13,149,151,163,17,181,19,2003,22,4,
%T A288519 6,16,10,64,14,166,29,307,31,9,27,81,15,183,21,249,291,401,41,421,43,
%U A288519 443,457,461,47,487,491,503,55,25,53,205,265,305,35,415,59,601,61
%N A288519 a(n) = least k such that A080670(k) begins with n.
%C A288519 a(p) <= p for any prime p.
%C A288519 a(n) <= A018800(n) for any n > 0.
%H A288519 Rémy Sigrist, <a href="/A288519/b288519.txt">Table of n, a(n) for n = 1..10000</a>
%H A288519 Rémy Sigrist, <a href="/A288519/a288519_1.png">Scatterplot of the first 1000000 terms</a>
%H A288519 Rémy Sigrist, <a href="/A288519/a288519.gp.txt">PARI program for A288519</a>
%e A288519 The following table shows the first values from A080670, as well as the terms that can be derived from it:
%e A288519 k       A080670(k)      Derived terms
%e A288519 --      ----------      -------------
%e A288519 1       1               a(1) = 1
%e A288519 2       2               a(2) = 2
%e A288519 3       3               a(3) = 3
%e A288519 4       22              a(22) = 4
%e A288519 5       5               a(5) = 5
%e A288519 6       23              a(23) = 6
%e A288519 7       7               a(7) = 7
%e A288519 8       23              none
%e A288519 9       32              a(32) = 9
%e A288519 10      25              a(25) = 10
%e A288519 11      11              a(11) = 11
%e A288519 12      223             a(223) = 12
%e A288519 13      13              a(13) = 13
%e A288519 14      27              a(27) = 14
%e A288519 15      35              a(35) = 15
%e A288519 16      24              a(24) = 16
%e A288519 17      17              a(17) = 17
%e A288519 18      232             a(232) = 18
%e A288519 19      19              a(19) = 19
%e A288519 20      225             a(225) = 20
%e A288519 21      37              a(37) = 21
%e A288519 22      211             a(211) = 22, a(21) = 22
%e A288519 23      23              none
%e A288519 24      233             a(233) = 24
%e A288519 25      52              a(52) = 25
%t A288519 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 *)
%Y A288519 Cf. A018800, A080670.
%K A288519 nonn,base,look
%O A288519 1,2
%A A288519 _Rémy Sigrist_, Jun 10 2017