A032664 -id:A032664 - cp's OEIS frontend

A032667 Digit '4' concatenated with a(n) is a prime.

1, 3, 7, 19, 21, 31, 33, 39, 43, 49, 57, 61, 63, 67, 79, 87, 91, 99, 111, 127, 129, 133, 139, 153, 157, 159, 177, 201, 211, 217, 219, 229, 231, 241, 243, 253, 259, 261, 271, 273, 283, 289, 297, 327, 337, 339, 349, 357, 363, 373, 391, 397, 409

Offset: 1

Patrick De Geest, May 15 1998

Obviously there can be no even terms in this sequence. - Alonso del Arte, Jun 18 2017

			Concatenate 4 and 1 to get 41, which is prime, so 1 is in the sequence.
Concatenate 4 and 3 to get 43, which is prime, so 3 is in the sequence.
Concatenate 4 and 5 to get 45 = 3^2 * 5, which is not prime, so 5 is not in the sequence.

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1740 from Vincenzo Librandi)

Cf. other digit 'd' concatenated with a(n) is prime sequences: A032664 (d = 1), A032665 (d = 2), A032666 (d = 3), A032668 (d = 5), A032669 (d = 6), A032670 (d = 7), A032671 (d = 8), A032672 (d = 9), A000040 (d = 0).

Select[2Range[250] - 1, PrimeQ[FromDigits[Join[{4}, IntegerDigits[#]]]] &] (* Alonso del Arte, Jun 18 2017 *)

isok(n) = isprime(eval(concat(4, Str(n)))); \\ Michel Marcus, Jun 19 2017

Offset adjusted at the suggestion of Michel Marcus by Alonso del Arte, Jun 18 2017

A167716 Squares that become a prime number when prefixed with a 1.

Original entry on oeis.org

1, 9, 49, 81, 289, 361, 1369, 1681, 2401, 2601, 2809, 3249, 3721, 4489, 5329, 6561, 6889, 7569, 7921, 9801, 10609, 14161, 14641, 19321, 19881, 21609, 22201, 25921, 32761, 35721, 36481, 40401, 41209, 47089, 49729, 52441, 61009, 67081, 77841

Offset: 1

Claudio Meller, Nov 10 2009

Subsequence of squares of A032664. - Michel Marcus, Jun 21 2016

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A032664.

Select[Range[1, 700, 2]^2, PrimeQ[FromDigits[Join[{1}, IntegerDigits[#]]]] &] (* G. C. Greubel, Jun 21 2016 *)
Select[Range[1,701,2]^2,PrimeQ[10^IntegerLength[#]+#]&] (* Harvey P. Dale, Mar 31 2019 *)

A166733 Numbers n with the property that the concatenation of the trivial divisors of n (i.e., 1 and n) is a prime.

Original entry on oeis.org

3, 7, 9, 13, 27, 31, 37, 39, 49, 51, 57, 63, 67, 73, 79, 81, 91, 93, 97, 99, 103, 109, 117, 123, 129, 151, 153, 163, 171, 181, 187, 193, 201, 213, 217, 223, 229, 231, 237, 249, 259, 277, 279, 283, 289, 291, 297, 301, 303, 307, 319, 321, 327, 361, 367, 373, 381

Offset: 1

Juri-Stepan Gerasimov, Oct 20 2009

Essentially the same as A032664. - R. J. Mathar, Oct 23 2009

			3 -> 13; 7 -> 17; 9 -> 19; 13 -> 113.

Cf. A120712.

Edited by Charles R Greathouse IV, Apr 24 2010

cp's OEIS Frontend

A032667 Digit '4' concatenated with a(n) is a prime.

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A167716 Squares that become a prime number when prefixed with a 1.

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Programs

Mathematica

A166733 Numbers n with the property that the concatenation of the trivial divisors of n (i.e., 1 and n) is a prime.

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