A072428 Numbers n for which there are exactly four k such that n = k + reverse(k).

44, 165, 404, 424, 444, 464, 484, 504, 524, 544, 564, 584, 1331, 1515, 1535, 1555, 1575, 1595, 1615, 1635, 1655, 1675, 1695, 2112, 2651, 3872, 4004, 5984, 13031, 13231, 13431, 13631, 13831, 14031, 14231, 14431, 14631, 14831, 15015, 16995

Offset: 1

Author

Klaus Brockhaus, Jun 17 2002

Keywords

• base
• nonn

Comments

Subsequence of A067030. First term is A072041(4).

Includes 4*(10^k+1) for k>=1. - Robert Israel, Jul 12 2019

Examples

			44 = k + reverse(k) for k = 13, 22, 31, 40; 1331 = k + reverse(k) for k = 1030, 1120, 1210, 1300.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..441
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A067030, A072041.

Programs

ARIBAS

var n,k,c,i,rev: integer; st,nst: string; end; m := 4; for n := 0 to 20000 do k := n div 2; c := 0; while k <= n and c < m + 1 do st := itoa(k); nst := ""; for i := 0 to length(st) - 1 do nst := concat(st[i],nst); end; rev := atoi(nst); if n = k + rev then inc(c); if k mod 10 <> 0 and k <> rev then inc(c); end; end; inc(k); end; if c = m then write(n,","); end; end;

Maple

N:= 10^5:
revdigs:= proc(n) local L, i;
  L:= convert(n, base, 10);
  add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
V:= Vector(N):
for x from 1 to N do
  v:= x + revdigs(x);
  if v <= N then V[v]:= V[v]+1 fi;
od:
select(t -> V[t]=4, [$1..N]); # Robert Israel, Jul 12 2019

Extensions

Offset changed by Robert Israel, Jul 12 2019