Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #54 Dec 10 2023 18:08:32
%S 1,10,40,81,90,100,121,160,250,252,360,400,403,484,490,574,640,736,
%T 765,810,900,976,1000,1008,1089,1207,1210,1300,1458,1462,1600,1612,
%U 1729,1855,1936,1944,2268,2296,2430,2500,2520,2668,2701,2944,3025,3154,3478,3600,3627,3640,4000,4030,4032,4275
%N 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.
%C Subsequence of A305231. This sequence excludes for example 4 = (s(4) + (-2)) * (s(4) + (-2)) from that sequence. - _David A. Corneth_, Apr 15 2019
%H David A. Corneth, <a href="/A306830/b306830.txt">Table of n, a(n) for n = 1..17624</a>
%H Viorel Nitica, Andrei Török, <a href="https://arxiv.org/abs/1908.00713">About Some Relatives of Palindromes</a>, arXiv:1908.00713 [math.NT], 2019.
%H Viorel Niţică, Jeroz Makhania, <a href="https://doi.org/10.3390/sym11111374">About the Orbit Structure of Sequences of Maps of Integers</a>, Symmetry (2019), Vol. 11, No. 11, 1374.
%e The sum of the digits of 90 is 9 and (9+21)*reversal(9+21) = 30*3 = 90, so 90 is in the sequence.
%e The sum of the digits of 2268 is 18 and (18 + 18)*reversal(18 + 18) = 36*63 = 2268, so 2268 is in the sequence.
%t 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 *)
%o (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
%o (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
%Y Cf. A004086 (reversal), A007953 (sum of digits), A027750 (divisors), A305231.
%K nonn,base
%O 1,2
%A _Viorel Nitica_, Mar 12 2019
%E Name clarified by _David A. Corneth_, Apr 15 2019