A275797 Primes for which the concatenation of the digits in the even positions and the concatenation of the digits in the odd positions are squares.

11, 19, 41, 409, 419, 449, 499, 811, 1061, 1069, 1861, 2459, 2851, 3061, 3469, 4091, 4099, 6449, 6841, 8011, 8419, 10211, 11261, 12251, 12659, 13669, 14699, 16649, 18211, 20809, 20849, 20899, 22859, 23869, 26849, 38611, 42451, 44491, 46441, 52259, 53269, 56249

Offset

1,1

Links

Michael De Vlieger, Table of n, a(n) for n = 1..1000

Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Classes of Gap Balancing Numbers, arXiv:1810.07895 [math.NT], 2018.

Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Counting families of generalized balancing numbers, The Australasian Journal of Combinatorics (2020) Vol. 77, Part 3, 318-325.

Example

419 is prime and numbers 49 and 1 are square.
12659 is prime and numbers 169 and 25 are square.

Mathematica

halfQ[n_, k_] := IntegerQ[Sqrt[FromDigits[IntegerDigits[n][[k ;; -1 ;; 2]]]]];
Select[Range[200000], PrimeQ[#] && halfQ[#, 1] && halfQ[#, 2] &] (* Amiram Eldar, Nov 05 2018 *)

Prog

(Perl) use ntheory ':all'; forprimes { my @d = split(//, $_); if (is_square(join('', map { $d[2*$_] } (0..$#d/2))) && is_square(join('', map { $d[2*$_+1] } (0..@d/2-1)))) { print "$_, " } } 10**6; # Daniel Suteu, Dec 03 2018
(PARI) isok(p) = {if (isprime(p), my (d=digits(p)); if (#d > 1, if (#d % 2, lo = #d\2+1; le = #d\2, le = #d\2; lo = #d\2); issquare(fromdigits(vector(le, k, d[2*k]))) && issquare(fromdigits(vector(lo, k, d[2*k-1]))); ); ); } \\ Michel Marcus, Dec 05 2018

Crossrefs

Cf. A000040, A000290.

Sequence in context: A167535 A184328 A260271 * A294993 A201719 A107201

Adjacent sequences: A275794 A275795 A275796 * A275798 A275799 A275800

Keyword

nonn,base

Author

Marius A. Burtea, Oct 26 2018

Status

approved