A306830 Integers k for which there exists a nonnegative integer j such that (s(k) + j) * reversal(s(k) + j) = k where s(k) is the sum of digits of k.

1, 10, 40, 81, 90, 100, 121, 160, 250, 252, 360, 400, 403, 484, 490, 574, 640, 736, 765, 810, 900, 976, 1000, 1008, 1089, 1207, 1210, 1300, 1458, 1462, 1600, 1612, 1729, 1855, 1936, 1944, 2268, 2296, 2430, 2500, 2520, 2668, 2701, 2944, 3025, 3154, 3478, 3600, 3627, 3640, 4000, 4030, 4032, 4275

Offset

1,2

Comments

Subsequence of A305231. This sequence excludes for example 4 = (s(4) + (-2)) * (s(4) + (-2)) from that sequence. - David A. Corneth, Apr 15 2019

Links

David A. Corneth, Table of n, a(n) for n = 1..17624

Viorel Nitica, Andrei Török, About Some Relatives of Palindromes, arXiv:1908.00713 [math.NT], 2019.

Viorel Niţică, Jeroz Makhania, About the Orbit Structure of Sequences of Maps of Integers, Symmetry (2019), Vol. 11, No. 11, 1374.

Example

The sum of the digits of 90 is 9 and (9+21)*reversal(9+21) = 30*3 = 90, so 90 is in the sequence.
The sum of the digits of 2268 is 18 and (18 + 18)*reversal(18 + 18) = 36*63 = 2268, so 2268 is in the sequence.

Mathematica

okQ[k_] := Module[{s, j}, s = Total[IntegerDigits[k]]; For[j = 0, j<k, j++, If[(s+j)IntegerReverse[s+j] == k, Print["k = ", k , ", j = ", j]; Return[ True]]]; False]; Reap[Do[If[okQ[k], Sow[k]], {k, 1, 4275}]][[2, 1]] (* Jean-François Alcover, Mar 17 2019 *)

Prog

(PARI) isok(k) = {my(s = sumdigits(k)); fordiv(k, d, if ((d>=s) && (k/d == fromdigits(Vecrev(digits(d)))), return (1)); ); return (0); } \\ Michel Marcus, Mar 13 2019
(PARI) upto(n) = {my(res = List([1, 10, 40, 81, 90]), m = 0); for(i = 10, 10*sqrtint(n), revi = fromdigits(Vecrev(digits(i))); if(revi <= i && i * revi <= n, m = i; listput(res, i * revi); ) ); q = #res; for(i = 1, #q, for(j = 1, logint(n \ res[i], 10), listput(res, res[i]*10^j); ) ); listsort(res, 1); res } \\ David A. Corneth, Apr 15 2019

Crossrefs

Cf. A004086 (reversal), A007953 (sum of digits), A027750 (divisors), A305231.

Sequence in context: A108777 A000132 A328093 * A305131 A217073 A210376

Adjacent sequences: A306827 A306828 A306829 * A306831 A306832 A306833

Keyword

nonn,base

Author

Viorel Nitica, Mar 12 2019

Extensions

Name clarified by David A. Corneth, Apr 15 2019

Status

approved