A072431 Numbers n for which there are exactly seven k such that n = k + reverse(k).

77, 132, 707, 727, 747, 767, 787, 807, 827, 847, 867, 887, 1212, 1232, 1252, 1272, 1292, 1312, 1332, 1352, 1372, 1392, 1661, 2321, 7007, 8987, 12012, 13992, 16061, 16261, 16461, 16661, 16861, 17061, 17261, 17461, 17661, 17861, 18678, 19338

Offset: 1

Author

Klaus Brockhaus, Jun 17 2002

Keywords

• base
• nonn

Comments

Subsequence of A067030. First term is A072041(7).

Examples

			77 = k + reverse(k) for k = 16, 25, 34, 43, 52, 61, 70; 132 = k + reverse(k) for k = 39, 48, 57, 66, 75, 84, 93.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..254
• 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 := 7; for n := 0 to 22600 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;

Mathematica

f[n_] := n + FromDigits@ Reverse@ IntegerDigits@ n; fQ[n_] := Block[{c = 0, k = 1}, While[k < n && n != f@ k, k++]; While[k < n, If[n == f@ k, c++]; k += 9]; c == 7]; Select[ Range@ 20000, fQ]
revAdd[n_] := n + FromDigits[Reverse[IntegerDigits[n]]]; ra=Table[revAdd[n], {n, 0, 10^5}]; t=Sort[Tally[ra]]; First /@ Select[t, #[[2]] == 7 && #[[1]] < Length[ra] &]