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

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, 56, 31, 60, 10, 63, 11, 216, 51, 69, 71, 73, 12, 76, 34, 79, 13, 82, 14, 86, 88, 89, 15, 93, 35, 96, 36, 98, 16, 100, 102, 103, 37, 107, 17, 110, 18, 257, 38, 116

Offset: 0

Author

Labos Elemer, Apr 03 2003

Keywords

• base
• nonn

Examples

			0 appears first in 26th prime (101), so a(0) = 26;
9 appears first in 8th prime (19), so a(9) = 8;
24 appears first in 53rd prime (241), so a(24) = 53.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 0..10000
• Index entries for primes involving decimal expansion of n

Crossrefs

Cf. A030000, A062584, A088781.

Programs

Mathematica

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 *)

Formula

A062584(n) = prime(a(n)). - Giovanni Resta, Apr 29 2017

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

Extensions

Data corrected by Giovanni Resta, Apr 29 2017

Name clarified by Pontus von Brömssen, Nov 29 2024