A229549 -id:A229549 - cp's OEIS frontend

A334533 Numbers k such that k*sod(k) and k/sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

1, 2, 3, 42, 26664, 2640264, 26400264, 264000264, 2640000264, 26400000264, 264000000264, 2640000000264, 26400000000264, 144689999986441, 154698898896451, 226589999985622, 234779999977432, 243788999887342, 244788898887442, 253698898896352, 254689878986452

Offset: 1

Giovanni Resta, May 05 2020

Intersection of A229549 and A334416.

264*(10^m+1) for m = 2 and m > 3 are terms. Among the first 1000 terms, most terms are palindromes or near-palindromes. The only terms where the first digit is not the same as the last digit among the first 1000 terms are: 42, 7458941369406538 and terms of the form 264*(10^m+1). - Chai Wah Wu, May 12 2020

			The sum of digits of 26664 is 24 and 26664*24  = 639936 and 26664/24 = 1111 are palindromes, so 26664 is a term.

Chai Wah Wu, Table of n, a(n) for n = 1..10001 (n = 1..1000 from Giovanni Resta)

Cf. A007953, A229549, A334416.

Select[Range[2.7*^6], (s = Plus @@ IntegerDigits[#]; Mod[#, s] == 0 && PalindromeQ[# s] && PalindromeQ[# /s]) &]

ispal(k) = my(d=digits(k)); d==Vecrev(d);
isok(k) = my(s=sumdigits(k)); !(k%s) && ispal(k/s) && ispal(k*s); \\ Michel Marcus, May 05 2020

A229805 Palindromes m such that m*(sum of digits of m) is also a palindrome.

Original entry on oeis.org

0, 1, 2, 3, 11, 22, 101, 111, 121, 202, 272, 353, 434, 515, 616, 888, 1001, 1111, 2002, 10001, 10101, 10201, 10901, 11011, 11111, 11711, 12521, 13331, 14141, 20002, 20702, 21512, 22322, 23132, 30503, 31313, 32123, 40304, 41114, 50105, 100001, 101101, 110011, 111111, 200002, 888888

Offset: 1

Derek Orr, Sep 29 2013

Palindromes in the sequence A229549.

			888*(8+8+8) = 21312 (another palindrome). So, 888 is a member of this sequence.

Giovanni Resta, Table of n, a(n) for n = 1..1000

Cf. A229549, A007953.

palQ[n_]:=Module[{idn=IntegerDigits[n],idn2},idn2=IntegerDigits[ n*Total[ idn]];idn==Reverse[idn]&&idn2==Reverse[idn2]]; Select[Range[ 0,33000], palQ] (* Harvey P. Dale, May 20 2014 *)

pal(n)=d=digits(n);Vecrev(d)==d
for(n=0,10^6,s=sumdigits(n);if(pal(n)*pal(n*s),print1(n,", "))) \\ Derek Orr, Apr 05 2015

def pal(n):
  r = ''
  for i in str(n):
    r = i + r
  return r == str(n)
def DS(n):
  s = 0
  for i in str(n):
    s += int(i)
  return s
{print(n, end=', ') for n in range(10**6) if pal(n)*pal(n*DS(n))}
## Simplified by Derek Orr, Apr 05 2015

A334661 Numbers k such that k*sod(k) and k+sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

Original entry on oeis.org

0, 1, 2, 3, 124, 829, 186373637, 186454637, 187272737, 195454547, 23212121199, 23302120299, 1230303030288, 1312121212098, 1320303030198, 1321121211198, 1321203021198, 1321211121198, 1330121210298, 1330203020298, 1330211120298, 1330301030298, 2130303030279

Offset: 1

Giovanni Resta, May 07 2020

For the first 2729 terms, most of them have digit sum 33. The only terms a(n) for n <= 2729 for which the digit sum is not 33 are for n = 1,...,10, 716, 2194, 2195. - Chai Wah Wu, May 15 2020

			The sum of digits of 829 is 19 and 829*19 = 15751 and 829+19 = 848 are palindromes, so 829 is a term.

Chai Wah Wu, Table of n, a(n) for n = 1..2729

Intersection of A229549 and A229545.

Cf. A007953, A334533.

Select[Range[0, 999], (s = Plus @@ IntegerDigits[#]; PalindromeQ[# s] && PalindromeQ[# + s]) &]

ispal(n) = my(d=digits(n)); d == Vecrev(d);
isok(m) = my(s=sumdigits(m)); ispal(m*s) && ispal(m+s); \\ Michel Marcus, May 08 2020

A334822 Palindromes k such that k*sod(k) and k/sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

Original entry on oeis.org

1, 2, 3, 144689999986441, 154698898896451, 226589999985622, 234779999977432, 243788999887342, 244788898887442, 253698898896352, 254689878986452, 254788878887452, 254797797797452, 333878999878333, 334878898878433, 335598898895533, 336589878985633, 336688878886633

Offset: 1

Chai Wah Wu, May 12 2020

Intersection of A002113 and A229549 and A334416. Palindromes in A334533.

For the first 10000 terms, most of them have digit sum 91. The only terms a(n) for n <= 10000 for which the digit sum is not 91 are 1, 2, 3 and a(1076) = 426666666666666624. - Chai Wah Wu, May 15 2020

			35479654545697453 is a palindrome whose sum of digits is 91. 35479654545697453/91 = 389886313688983 and 35479654545697453*91 = 3228648563658468223 which are both palindromes. So 35479654545697453 is a term.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A002113, A007953, A229549, A334416, A334533.

cp's OEIS Frontend

A334533 Numbers k such that k*sod(k) and k/sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

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A229805 Palindromes m such that m*(sum of digits of m) is also a palindrome.

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A334661 Numbers k such that k*sod(k) and k+sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

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A334822 Palindromes k such that k*sod(k) and k/sod(k) are both palindromes, where sod(k) denotes the sum of digits of k (A007953).

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