A328850 Squares in whose primorial base expansion only even digits appear.

0, 4, 16, 64, 144, 196, 484, 900, 1024, 1444, 1764, 2116, 2304, 4624, 5184, 5476, 6084, 6724, 13924, 14400, 14884, 18496, 19044, 20164, 23104, 23716, 24964, 28224, 29584, 61504, 65536, 66564, 70756, 73984, 79524, 80656, 85264, 88804, 90000, 121104, 131044, 135424, 139876, 186624, 195364, 204304, 209764, 242064, 260100, 264196

Offset

1,2

Comments

Squares in A328849, squares such that also the prime factor form (A276086) of their primorial base expansion is a square,

Links

Antti Karttunen, Table of n, a(n) for n = 1..390

Index entries for sequences related to primorial base.

Formula

a(n) = A000290(A328838(n)).

Example

12^2 = 144 is written as "4400" in primorial base (A049345), as 4*A002110(3) + 4*A002110(2) + 0*A002110(1) + 0*A002110(0) = 4*30 + 4*6 = 144, thus its prime code encoding, A276086(144) = prime(4)^4 * prime(3)^4 = 7^4 * 5^4 = 1500625 is also a square, and 144 is included in this sequence.

Mathematica

q[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; AllTrue[s, EvenQ]]; Select[Range[0, 520]^2, q] (* Amiram Eldar, Mar 06 2024 *)

Prog

(PARI)
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
isA328850(n) = (issquare(n) && issquare(A276086(n)));

Crossrefs

Cf. A328838 (gives the square roots).

Intersection of A000290 and A328849.

Cf. A002110, A010052, A049345, A276086.

Sequence in context: A275217 A158988 A337968 * A330687 A027676 A249567

Adjacent sequences: A328847 A328848 A328849 * A328851 A328852 A328853

Keyword

nonn,base

Author

Antti Karttunen, Oct 30 2019

Status

approved