A334533 -id:A334533 - cp's OEIS frontend

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).

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

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).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI