A053918
Numbers k such that k^2 contains only digits {2,3,5}.
Original entry on oeis.org
5, 15, 235, 485, 1885, 5765, 15885, 50235, 57665, 72335, 1798765, 15249765, 187703365, 179876492415, 159789024443333515, 576387476638096486959455635
Offset: 1
-
# see link for faster version
def aupto(limit):
alst = []
for k in range(1, limit+1):
if set(str(k*k)) <= set("235"): alst.append(k)
return alst
print(aupto(2*10**6)) # Michael S. Branicky, May 15 2021
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 03 2005
One more term from Mishima's webpage added by
Max Alekseyev, Jun 17 2011
A119152
Triangular numbers composed of digits {2,3,5}.
Original entry on oeis.org
3, 55, 253, 325, 5253, 255255, 2235555, 2355535, 3252525, 222552253, 225323523253, 33533553332223253, 523355323323222253, 252235353552533225335, 22323332525535322225335, 223533355523232355353232325353525335
Offset: 1
Original entry on oeis.org
25, 27, 32, 225, 2025, 2197, 2500, 3025, 3375, 7225, 11025, 13225, 21952, 22500, 27000, 27225, 55225, 70225, 112225, 133225, 172225, 195112, 202500, 207025, 235225, 250000, 255025, 302500, 319225, 511225, 555025, 570025, 722500, 1102500, 1113025, 1177225, 1311025
Offset: 1
32 is a term since A329147(21) = 32 = 2^5.
2197 is a term since A329147(194) = 2197 = 13^3.
235225 is a term since A329147(123113) = 235225 = 485^2.
Subsequences of squares with specified digits:
A058426 (0,2,5),
A053919 (2,3,5),
A030485 (2,5,7),
A191486 (2,3,5,7).
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p[n_] := If[n > 0, Prime[n], 0]; ppQ[n_] := GCD @@ FactorInteger[n][[;; , 2]] > 1; seq[ndigmax_] := Module[{t = Table[FromDigits[Flatten@ IntegerDigits@ (p /@ IntegerDigits[n])], {n, 0, 10^ndigmax - 1}]}, Union@ Select[t, 0 < # < 10^ndigmax && ppQ[#] &]]; seq[6] (* Amiram Eldar, Mar 26 2023 *)
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f(n) = if (n, fromdigits(concat(apply(d -> if (d, digits(prime(d)), [0]), digits(n)))), 0); \\ A329147
lista(nn) = my(list = List(), m); for (n=0, nn, m = f(n); if ((m <= nn) && ispower(m), listput(list, m));); vecsort(Set(list)); \\ Michel Marcus, Mar 26 2023
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