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

1,1

Comments

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

Links

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

Example

.    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 .

Prog

(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

Crossrefs

Cf. A000040, A091633, A136333.

Sequence in context: A082626 A344542 A334132 * A338715 A258190 A244471

Adjacent sequences: A245190 A245191 A245192 * A245194 A245195 A245196

Keyword

nonn,base

Author

Reinhard Zumkeller, Jul 18 2014

Status

approved