A235126 -id:A235126 - cp's OEIS frontend

A090713 Primes whose base-17 expansion is a (valid) decimal expansion of a prime.

2, 3, 5, 7, 37, 43, 71, 103, 109, 139, 347, 349, 443, 449, 619, 647, 683, 887, 919, 1259, 1571, 1601, 1607, 1741, 1873, 2083, 2347, 2417, 2659, 2689, 4933, 4967, 4973, 4999, 5651, 5783, 5821, 6163, 6673, 6803, 6971, 7079, 7243, 7351, 7591

Offset: 1

Cino Hilliard, Jan 18 2004

See A235126 for the corresponding primes whose base-10 representation is the base-17 representation of the terms here. - M. F. Hasler, Jan 05 2014

			The prime p = 37 is written 23 in base 17, and 23 is again a prime (when interpreted in base 10). Therefore p = 37 is a term of this sequence.

Robert Price, Table of n, a(n) for n = 1..3754

Cf. A090707 - A090721 and further references there.

is_A090713(p)=vecmax(d=digits(p,17))<10&&isprime(vector(#d,i,10^(#d-i))*d~)&&isprime(p) \\ - M. F. Hasler, Jan 05 2014

Edited by N. J. A. Sloane, Feb 07 2007, and by M. F. Hasler, Jan 03 2014

A235144 Primes whose base-10 representation also represents a prime in base 19.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 43, 47, 113, 131, 151, 157, 179, 199, 229, 263, 283, 311, 317, 353, 359, 409, 421, 443, 461, 557, 593, 641, 661, 739, 773, 809, 821, 881, 937, 953, 977, 1031, 1109, 1213, 1217, 1231, 1279, 1291, 1297, 1307, 1433, 1439, 1583, 1657, 1693, 1697, 1741, 1789, 1811, 1873, 1877, 1949, 1987, 2003

Offset: 1

M. F. Hasler, Jan 03 2014

See A090714 for a similar sequence whose definition works "in the opposite direction".

			The decimal representation of prime 23, considered as a number written in base 19, stands for 2*19 + 3 = 41, which is also prime, therefore 23 is in the sequence.

Robert Price, Table of n, a(n) for n = 1..3276

Cf. A235110, A235126 and other sequences in the range A090707 - A091924.

Select[Prime[Range[300]], PrimeQ[FromDigits[IntegerDigits[#], 19]] &] (* Alonso del Arte, Jan 04 2014 *)

is_A235144(p, b=19)={my(d=digits(p)); isprime(vector(#d, i, b^(#d-i))*d~)&&isprime(p)} \\ This code allows one to produce similar sequences for other bases b > 9 (which can be given as optional 2nd argument), but does not do the required check for bases b < 10.

cp's OEIS Frontend

A090713 Primes whose base-17 expansion is a (valid) decimal expansion of a prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Extensions