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

Author

Viorel Nitica, Mar 12 2019

Keywords

• nonn
• base

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

Examples

			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.
		

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.

Crossrefs

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

Programs

Mathematica

okQ[k_] := Module[{s, j}, s = Total[IntegerDigits[k]]; For[j = 0, jJean-François Alcover, Mar 17 2019 *)

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

Extensions

Name clarified by David A. Corneth, Apr 15 2019