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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.
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%I #13 Feb 27 2020 23:14:57

%S 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 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 9,16,14,18,4,60,18,18,18,64,18,66,8,68,69,40,10,6,1

%N 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 This sequence is a variant of A329428.

%H Rémy Sigrist, <a href="/A330356/b330356.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A330356/a330356_1.gp.txt">PARI program for A330356</a>

%F a(n) <= n with equality iff n belongs to A062115.

%F a(prime(k)) = a(k) for any k > 0 where prime(k) denotes the k-th prime number.

%F a(A007097(k)) = 1 for any k >= 0.

%e For n = 8601:

%e - let pi = A000720,

%e - 8601 gives 8 followed by pi(601) = 8110,

%e - 8110 gives pi(811) followed by 0 = 1410,

%e - 1410 gives 1 followed by pi(41) followed by 0 = 1130,

%e - 1130 gives pi(113) followed by 0 = 300,

%e - 300 gives pi(3) followed by 00 = 200,

%e - 200 gives pi(2) followed by 00 = 100,

%e - no prime number appears in 100,

%e - hence a(8601) = 100.

%o (PARI) See Links section.

%Y Cf. A000720, A007097, A062115, A327539, A329428.

%K nonn,base

%O 0,5

%A _Rémy Sigrist_, Dec 11 2019