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A330356 Starting from n: as long as the decimal representation contains a prime number, replace the largest and leftmost such substring with the index of the corresponding prime number; a(n) corresponds to the final value.

%I A330356 #13 Feb 27 2020 23:14:57
%S A330356 0,1,1,1,4,1,6,4,8,9,10,1,1,6,14,6,16,4,18,8,10,1,1,9,14,9,16,14,18,
%T A330356 10,10,1,1,9,14,9,16,1,18,10,40,6,6,14,44,14,46,6,48,49,10,1,1,16,14,
%U A330356 9,16,14,18,4,60,18,18,18,64,18,66,8,68,69,40,10,6,1
%N A330356 Starting from n: as long as the decimal representation contains a prime number, replace the largest and leftmost such substring with the index of the corresponding prime number; a(n) corresponds to the final value.
%C A330356 This sequence is a variant of A329428.
%H A330356 Rémy Sigrist, <a href="/A330356/b330356.txt">Table of n, a(n) for n = 0..10000</a>
%H A330356 Rémy Sigrist, <a href="/A330356/a330356_1.gp.txt">PARI program for A330356</a>
%F A330356 a(n) <= n with equality iff n belongs to A062115.
%F A330356 a(prime(k)) = a(k) for any k > 0 where prime(k) denotes the k-th prime number.
%F A330356 a(A007097(k)) = 1 for any k >= 0.
%e A330356 For n = 8601:
%e A330356 - let pi = A000720,
%e A330356 - 8601 gives 8 followed by pi(601) = 8110,
%e A330356 - 8110 gives pi(811) followed by 0 = 1410,
%e A330356 - 1410 gives 1 followed by pi(41) followed by 0 = 1130,
%e A330356 - 1130 gives pi(113) followed by 0 = 300,
%e A330356 - 300 gives pi(3) followed by 00 = 200,
%e A330356 - 200 gives pi(2) followed by 00 = 100,
%e A330356 - no prime number appears in 100,
%e A330356 - hence a(8601) = 100.
%o A330356 (PARI) See Links section.
%Y A330356 Cf. A000720, A007097, A062115, A327539, A329428.
%K A330356 nonn,base
%O A330356 0,5
%A A330356 _Rémy Sigrist_, Dec 11 2019