A376026 Numbers k such that the concatenation of k+1 and k^2 is prime.

17, 21, 27, 29, 51, 57, 63, 69, 71, 81, 87, 111, 113, 119, 123, 137, 149, 209, 227, 231, 233, 243, 263, 267, 303, 323, 369, 383, 407, 411, 447, 449, 453, 461, 479, 531, 551, 563, 567, 587, 593, 609, 617, 677, 689, 699, 701, 719, 771, 777, 813, 819, 827, 857, 881, 897, 909, 911, 929, 969, 987, 999

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 27 is a term because the concatenation of 27 + 1 = 28 and 27^2 = 729 is 28729, which is prime.

Maple

tcat:= (a, b) -> a*10^(ilog10(b)+1)+b:
select(t -> isprime(tcat(t+1, t^2)), [seq(i, i=1..1000, 2)]);

Mathematica

Select[Range[1000], PrimeQ[FromDigits[Join[IntegerDigits[#+1], IntegerDigits[#^2]]]] &] (* Stefano Spezia, Sep 06 2024 *)

Prog

(Python)
from sympy import isprime
def ok(n): return isprime(int(str(n+1)+str(n**2)))
print([k for k in range(10**3) if ok(k)]) # Michael S. Branicky, Sep 15 2024

Crossrefs

Sequence in context: A307863 A128546 A188200 * A060875 A259555 A050845

Adjacent sequences: A376023 A376024 A376025 * A376027 A376028 A376029

Keyword

nonn,base

Author

Robert Israel, Sep 06 2024

Status

approved