A361821 Perfect powers in A329150.

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

1,1

Comments

No term has a digit 4, 6 or 8.

Subsequences of squares are listed in Crossrefs.

Links

Table of n, a(n) for n=1..37.

Example

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.

Mathematica

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 *)

Prog

(PARI) 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

Crossrefs

Intersection of A001597 and A329150.

Cf. A329147.

Subsequences of squares with specified digits: A058426 (0,2,5), A053919 (2,3,5), A030485 (2,5,7), A191486 (2,3,5,7).

Sequence in context: A183982 A287763 A239523 * A129820 A096522 A195351

Adjacent sequences: A361818 A361819 A361820 * A361822 A361823 A361824

Keyword

nonn,base

Author

Bernard Schott, Mar 25 2023

Status

approved