cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A058425 Numbers k such that k^2 contains only digits {0,2,5}, not ending with zero.

Original entry on oeis.org

5, 15, 45, 235, 505, 745, 1415, 1485, 4495, 5005, 15985, 50005, 72495, 469255, 500005, 500505, 1597505, 1598515, 4474955, 5000005, 5000505, 5050005, 7085235, 15008515, 44949995, 50000005, 50000505, 50005005, 50500005, 500000005, 500000505, 500005005, 500254955, 500500005
Offset: 1

Views

Author

Patrick De Geest, Nov 15 2000

Keywords

Comments

Most terms have a special pattern in that they have only digits 0 and 5 and could be written as Sum_{h=0..t} 5*10^f(h), where 2f(h), 2f(h)-1, and f(h1) + f(h2) are all distinct and f(0)=0 for the nonzero ending constraint. - Zhao Hui Du, Mar 12 2024

Crossrefs

Cf. A058426.

Extensions

a(29)=50500005 inserted by Georg Fischer, Jan 12 2022

A119051 Triangular numbers composed of digits {0,2,5}.

Original entry on oeis.org

55, 5050, 25200, 255255, 500500, 50005000, 525220255, 2250500505, 5000050000, 22052205055, 500000500000, 520022025225, 2205022050055, 2225205025200, 5220005220550, 50000005000000, 220500220500055, 550250022200005, 2552552000225055, 5000000050000000
Offset: 1

Views

Author

Giovanni Resta, May 10 2006

Keywords

Crossrefs

Cf. A000217, A058426, A119052. See A119033 for a table of cross-references.

Formula

a(n) = A000217(A119052(n)). - Tyler Busby, Mar 31 2023

Extensions

a(19)-a(20) from Tyler Busby, Mar 22 2023

A361821 Perfect powers in A329150.

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

Views

Author

Bernard Schott, Mar 25 2023

Keywords

Comments

No term has a digit 4, 6 or 8.
Subsequences of squares are listed in Crossrefs.

Examples

			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.
		

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).

Programs

  • 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 *)
  • 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
Showing 1-3 of 3 results.