A262830 -id:A262830 - cp's OEIS frontend

A262829 (3,2)-primes (defined in Comments).

2, 3, 7, 13, 31, 37, 43, 67, 79, 151, 157, 181, 193, 223, 241, 271, 283, 307, 331, 349, 373, 397, 409, 421, 433, 463, 499, 571, 613, 619, 631, 643, 661, 673, 691, 733, 757, 769, 787, 829, 853, 877, 937, 997, 1009, 1093, 1123, 1129, 1153, 1201, 1213, 1231

Offset: 1

Clark Kimberling, Oct 24 2015

Let V = (b(1), b(2), ..., b(k)), where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p a V-prime if the digits of p in base b(1) spell a prime in each of the bases b(2), ..., b(k).

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A000040, A235266, A262730.

{b1, b2} = {2, 3};
u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235266 *)
v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &];  (* A262829 *)
w = Intersection[u, v]; (* A262830 *)
(* Peter J. C. Moses, Sep 27 2015 *)

A262832 {2,5}-primes (defined in Comments).

Original entry on oeis.org

2, 11, 13, 41, 151, 173, 181, 191, 223, 233, 241, 313, 331, 421, 443, 463, 541, 563, 641, 701, 733, 743, 953, 1373, 1451, 1471, 1483, 1753, 1783, 1831, 1993, 2011, 2143, 2161, 2351, 2411, 2693, 3041, 3061, 3491, 3571, 3623, 3761, 3943, 4051, 4373, 4643, 4813

Offset: 1

Clark Kimberling, Oct 31 2015

Let S = {b(1), b(2), ..., b(k)}, where k > 1 and b(i) are distinct integers > 1 for j = 1..k. Call p an S-prime if the digits of p in base b(i) spell a prime in each of the bases b(j) in S, for i = 1..k. Equivalently, p is an S-prime if p is a strong-V prime (defined at A262729) for every permutation of the vector V = (b(1), b(2), ..., b(k)).

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A000040, A262729, A235266, A262830.

{b1, b2} = {2, 5};
u = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b1], b2]] &]; (* A235475 *)
v = Select[Prime[Range[6000]], PrimeQ[FromDigits[IntegerDigits[#, b2], b1]] &]; (* A262831 *)
w = Intersection[u, v]; (* A262832 *)
(* Peter J. C. Moses, Sep 27 2015 *)

cp's OEIS Frontend

A262829 (3,2)-primes (defined in Comments).

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