A259541 Numbers n such that antisigma(n) is palindromic.

1, 2, 3, 4, 5, 6, 13, 23, 30, 31, 36, 109, 119, 158, 351, 1645, 1653, 2003, 3476, 3520, 3934, 4913, 8037, 9379, 35324, 36516, 91951, 128955, 200003, 390066, 402603, 1068869, 2000003, 2144992, 2467458, 2867828, 3392245, 3607663

Offset: 1

Author

Paolo P. Lava, Jun 30 2015

Keywords

• nonn
• base
• easy

Comments

Primes of the form 2*10^k+3 belong the sequence (see A177134 and A081677).

Examples

			antisigma(1) = 1*2/2 - sigma(1) = 1 - 1 = 0;
antisigma(13) = 13*14/2 - sigma(13) = 91 - 14 = 77;
antisigma(109) = 109*110/2 - sigma(109) = 5995 - 110 = 5885.
		

Crossrefs

Cf. A024816, A028980, A081677.

Programs

Maple

with(numtheory): T:=proc(w) local x, y, z; x:=w; y:=0;
for z from 1 to ilog10(x)+1 do y:=10*y+(x mod 10); x:=trunc(x/10);
od; y; end: P:=proc(q) local a,n;
for n from 1 to q do a:=n*(n+1)/2-sigma(n); if a=T(a) then print(n);
fi; od; end: P(10^9);

Mathematica

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; Select[Range@ 4000000, palQ[# (# + 1)/2 - DivisorSigma[1, #]] &] (* Michael De Vlieger, Jul 01 2015 *)

PARI

isok(n) = my(d = digits(n*(n+1)/2 - sigma(n))); Vecrev(d)==d; \\ Michel Marcus, Jul 01 2015