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

1,2

Comments

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

Links

Table of n, a(n) for n=1..38.

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A024816, A028980, A081677.

Sequence in context: A200330 A121433 A317778 * A274838 A200331 A010349

Adjacent sequences: A259538 A259539 A259540 * A259542 A259543 A259544

Keyword

nonn,base,easy

Author

Paolo P. Lava, Jun 30 2015

Status

approved