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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
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
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
KEYWORD
nonn,base
AUTHOR
Viorel Nitica, Mar 12 2019
EXTENSIONS
Name clarified by David A. Corneth, Apr 15 2019
STATUS
approved