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
Examples
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.
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Programs
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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 *) -
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)));
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