A072443 -id:A072443 - cp's OEIS frontend

A077760 Numbers which in at least two ways are the product of two distinct numbers with the same digits (leading zeros are forbidden).

101556, 121968, 124012, 133875, 144648, 172900, 185472, 226800, 352170, 433755, 2096640, 3779136, 4264416, 5166504, 5333680, 5448960, 5651919, 5894784, 5955264, 5983936, 6003088, 6174630, 6197724, 6324318, 6351840, 6429600, 6494400, 6514060, 6794424, 6874560, 7064496

Offset: 1

Klaus Brockhaus, Nov 14 2002

			101556 = 156*651 = 273*372; 2096640 = 1092*1920 = 1365*1536.

David A. Corneth, Table of n, a(n) for n = 1..10408 (terms <= 2*10^10)

Cf. A000037, A072443.

{for(n=100, 6500000,  my(k=logint(n,100), f=divisors(n), v=[]); for(h=1, matsize(f)[2], if(10^k1, my(w=[]); for(i=1, b, my(s=[], a=v[i]); while(a>0, my(d=divrem(a, 10)); a=d[1]; s=concat(d[2], s)); w=concat(w, [vecsort(s)])); my(c=0); for(i=1, b-1, for(j=i+1, b, if(c<2&&w[i]==w[j], if(v[i]*v[j]==n, if(c==1, print1(n, ", "); c=2, c=1)))))))}

Offset changed to 1 by and more terms from David A. Corneth, Sep 08 2024

Name corrected by Sean A. Irvine, Jun 11 2025

A129623 Numbers which are the product of a non-palindrome and its reversal, where leading zeros are not allowed.

Original entry on oeis.org

252, 403, 574, 736, 765, 976, 1008, 1207, 1300, 1458, 1462, 1612, 1729, 1855, 1944, 2268, 2296, 2430, 2668, 2701, 2944, 3154, 3478, 3627, 3640, 4032, 4275, 4606, 4930, 5092, 5605, 5848, 6624, 6786, 7663, 8722, 20502, 23632, 26962, 30492, 31003, 34222

Offset: 1

Tanya Khovanova, May 30 2007

The smallest square in this sequence is 63504 = 252*252 = 144*441.

			252 = 12*21.

Michael S. Branicky, Table of n, a(n) for n = 1..11195 (terms < 10^9)

Cf. A072443, A076750.

Take[Union[ Transpose[ Select[Table[{n, n* FromDigits[Reverse[IntegerDigits[n]]]}, {n, 1000}], Mod[ #[[1]], 10] != 0 && #[[1]] != FromDigits[Reverse[IntegerDigits[ #[[1]]]]] &]][[2]]], 100]
upto2ndigits@n_ := Union@(If[(i = IntegerReverse@#) > #, i*#, Nothing] & /@Range@(10^n - 1)); upto2ndigits@3 (* Hans Rudolf Widmer, Sep 06 2024 *)

from sympy import divisors
def ok(n): return any(n==d*int(s[::-1]) for d in divisors(n)[1:-1] if (s:=str(d))!=s[::-1] and s[-1]!="0")
print([k for k in range(36000) if ok(k)]) # Michael S. Branicky, Sep 07 2024

# instantly generates 44185 terms with n = 5
def aupto2ndigits(n): return(sorted(set(i*int(s[::-1]) for i in range(12, 10**n) if i%10 != 0 and (s:=str(i)) != s[::-1])))
print(aupto2ndigits(2))
# Michael S. Branicky, Sep 08 2024 after Hans Rudolf Widmer

Offset corrected by Stefano Spezia, Sep 07 2024

cp's OEIS Frontend

A077760 Numbers which in at least two ways are the product of two distinct numbers with the same digits (leading zeros are forbidden).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Extensions