A246422 -id:A246422 - cp's OEIS frontend

A238712 Numbers in which squares may end (in base 10).

0, 1, 4, 5, 6, 9, 16, 21, 24, 25, 29, 36, 41, 44, 49, 56, 61, 64, 69, 76, 81, 84, 89, 96, 100, 104, 116, 121, 124, 129, 136, 144, 156, 161, 164, 169, 176, 184, 196, 201, 204, 209, 216, 224, 225, 236, 241, 244, 249, 256, 264, 276, 281, 284, 289, 296, 304

Offset: 1

M. F. Hasler, Mar 03 2014

The union of "squares mod 10" (= the first 6 terms) and "squares mod 100" (A010461) and "squares mod 1000" (A122986) etc.

The number of terms < 10^k beginning with k=0: 1, 6, 24, 165, 1101, 9306, 79620, 753462, 7198791, 70919559, ... - Robert G. Wilson v, Sep 04 2014

			6 is in the sequence because 4^2 = 16 ends in the digit 6.
7 is not in the sequence because no square can end with the digit 7.

Derek Orr, Table of n, a(n) for n = 1..9306

Cf. A161355, A246422, A246448 (Complement).

mx = 3; t = Union@ Table[ Mod[n^2, 10^mx], {n, 10^mx/2}]; t = Union@ Flatten@ Table[ Mod[t, 10^m], {m, mx}] (* Robert G. Wilson v, Sep 04 2014 *)

a=[];for(m=1,3,a=setunion(a,Set(vector(10^m,n,n^2)%10^m)));a

If n is present so is n^2. - Robert G. Wilson v, Sep 04 2014

A246449 Numbers k such that no cube can end in k (in the sense of the respective decimal expansions).

Original entry on oeis.org

10, 14, 15, 18, 20, 22, 26, 30, 34, 35, 38, 40, 42, 45, 46, 50, 54, 55, 58, 60, 62, 65, 66, 70, 74, 78, 80, 82, 85, 86, 90, 94, 95, 98, 100, 102, 105, 106, 108, 110, 114, 115, 116, 118, 120, 122, 124, 126, 130, 132, 134, 135, 138, 140, 142, 145, 146, 148, 150, 154, 155

Offset: 1

Derek Orr, Aug 26 2014

Complement of A246422.

The terms with n digits are the complement in [10^(n-1) .. 10^n-1] of the set of residues of k^3 mod 10^n for 10^((n-1)/3) < k < 10^n. - M. F. Hasler, Jan 26 2020

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A246422.

seq(op(sort(convert({$10^(d-1)..10^d-1} minus map(t -> t^3 mod 10^d, {$0..10^d-1}),list))),d=1..3); # Robert Israel, Jan 26 2020

v=vector(1000); for(k=1,10^4, my(q=k^3,w=digits(q));for(j=0,2, v[1+fromdigits(w[#w-j..#w])]++)); for(k=1,160, if(v[k]==0,print1(k-1,", "))) \\ Hugo Pfoertner, Jan 26 2020

A246449_row(n)=setminus([10^(n-1)..10^n-1],Set([k^3|k<-[sqrtnint(10^(n-1),3)+1..10^n-1]]%10^n)) \\ Yields the n-digit terms. - M. F. Hasler, Jan 26 2020

from sympy import nthroot_mod
from itertools import count, islice
def A246449_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda n: nthroot_mod(n,3,10**(len(str(n)))) is None, count(max(startvalue,0)))
A246449_list = list(islice(A246449_gen(),20)) # Chai Wah Wu, Feb 16 2023

Corrected by Robert Israel, Jan 26 2020

Name edited and incorrect PARI program deleted by M. F. Hasler, Jan 26 2020

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A238712 Numbers in which squares may end (in base 10).

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A246449 Numbers k such that no cube can end in k (in the sense of the respective decimal expansions).

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