A245193 Smallest prime having in decimal representation A136333(n) as suffix.

11, 3, 7, 19, 11, 13, 17, 19, 31, 233, 37, 139, 71, 73, 277, 79, 191, 193, 97, 199, 2111, 113, 1117, 3119, 131, 4133, 137, 139, 1171, 173, 4177, 179, 191, 193, 197, 199, 311, 313, 317, 1319, 331, 2333, 337, 2339, 2371, 373, 2377, 379, 3391, 2393, 397, 1399

Offset: 1

Author

Reinhard Zumkeller, Jul 18 2014

Keywords

• nonn
• base

Comments

a(n) = A136333(n) iff A136333(n) itself is a prime number, cf. A091633.

Examples

			.    n  |   a(n)  | A136333(n)
. ------+---------+-----------
.   10  |    233  |      33
.   11  |     37  |      37
.   12  |    139  |      39
.   13  |     71  |      71
.   14  |     73  |      73
.   15  |    277  |      77
.   16  |     79  |      79
.   17  |    191  |      91
.   18  |    193  |      93
.   19  |     97  |      97
.   20  |    199  |      99
.   21  |   2111  |     111
.   22  |    113  |     113
.   23  |   1117  |     117
.   24  |   3119  |     119
.   25  |    131  |     131
.   26  |   4133  |     133
.   27  |    137  |     137
.   28  |    139  |     139
.   29  |   1171  |     171
.   30  |    173  |     173 .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A091633, A136333.

Programs

Haskell

import Data.List (isSuffixOf); import Data.Function (on)
a245193 n = head [p | p <- a000040_list,
                      (isSuffixOf `on` show) (a136333 n) p]

PARI

isok(m) = my(d=digits(m)); apply(x->gcd(x, 10), d) == vector(#d, k, 1); \\ A136333
f(m) = my(p=nextprime(m), s=10^#Str(m)); while ((p-m) % s, p = nextprime(p+1)); p;
lista(nn) = apply(x->f(x), select(isok, [1..nn]));
lista(1000) \\ Michel Marcus, Feb 25 2022