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A082058 a(n) is the smallest k such that prime(k) contains the digits of n as a substring.

%I A082058 #16 Nov 29 2024 21:15:42
%S A082058 26,5,1,2,13,3,18,4,23,8,26,5,31,6,35,36,38,7,42,8,197,47,48,9,53,54,
%T A082058 56,31,60,10,63,11,216,51,69,71,73,12,76,34,79,13,82,14,86,88,89,15,
%U A082058 93,35,96,36,98,16,100,102,103,37,107,17,110,18,257,38,116
%N A082058 a(n) is the smallest k such that prime(k) contains the digits of n as a substring.
%H A082058 Giovanni Resta, <a href="/A082058/b082058.txt">Table of n, a(n) for n = 0..10000</a>
%H A082058 <a href="/index/Pri#piden">Index entries for primes involving decimal expansion of n</a>
%F A082058 A062584(n) = prime(a(n)). - _Giovanni Resta_, Apr 29 2017
%F A082058 a(n) >= A088781(n) for n >= 1. The smallest positive n for which a(n) > A088781(n) is 114. - _Pontus von Brömssen_, Nov 29 2024
%e A082058 0 appears first in 26th prime (101), so a(0) = 26;
%e A082058 9 appears first in 8th prime (19), so a(9) = 8;
%e A082058 24 appears first in 53rd prime (241), so a(24) = 53.
%t A082058 tg=101; T=0*Range[tg]; k=0; subs[n_] := Block[{d = IntegerDigits[n]}, Flatten@ Table[ FromDigits@ Take[d, {i, j}], {j, Length[d]}, {i, j}]]; While[tg > 0, s = subs[Prime[++k]]; Do[ If[e <= 100 && T[[e+1]] == 0, T[[e+1]] = k; tg--], {e, s}]]; T (* _Giovanni Resta_, Apr 29 2017 *)
%Y A082058 Cf. A030000, A062584, A088781.
%K A082058 base,nonn
%O A082058 0,1
%A A082058 _Labos Elemer_, Apr 03 2003
%E A082058 Data corrected by _Giovanni Resta_, Apr 29 2017
%E A082058 Name clarified by _Pontus von Brömssen_, Nov 29 2024