A258413 Numbers m such that antisigma(m) contains sigma(m) as a substring.

34, 79, 479, 1529, 2879, 4895, 8873, 14243, 26879, 62498, 79999, 295285, 559571, 589219, 644735, 799999, 2012897, 2181600, 2233033, 2395488, 6399839, 7453541, 7922023, 8598719, 22928034, 26861727, 37894930, 55056372, 63652895, 76820471, 144726608, 174044214

Offset: 1

Author

Paolo P. Lava, May 29 2015

Keywords

• nonn
• base

Comments

Prime numbers in the sequence: 79, 479, 2879, 14243, 26879, 79999, 559571, 589219, ...

The primes of the form 8*10^k-1, for k>0, like 79 or 79999, are terms. See A056721. - Giovanni Resta, Jun 08 2015

Examples

			sigma(34) = 54 and antisigma(34) = 34*35/2 - 54 = 541, which contains 54 as a substring;
sigma(79) = 80 and antisigma(79) = 79*80/2 - 80 = 3080, which contains 80 as a substring;
sigma(479) = 480 and antisigma(479) = 479*480/2 - 480 = 114480, which contains 480 as a substring.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..55 (terms < 6*10^10)

Crossrefs

Cf. A000203, A024816, A255968, A056721.

Programs

Maple

with(numtheory): P:=proc(q) local a,b,c,d,j,k,n;
for n from 1 to q do a:=sigma(n); c:=ilog10(a)+1; b:=n*(n+1)/2-sigma(n); d:=ilog10(b)+1; for k from 0 to d-c do j:=trunc(b/10^k);
if a=j-trunc(j/10^c)*10^c then print(n); break; fi; od; od; end: P(10^9);

Mathematica

fQ[n_]:=StringMatchQ[ToString[n*(n+1)/2-DivisorSigma[1,n]],_~~ToString[DivisorSigma[1,n]]~~_];Select[Range[10^5],fQ[#]&] (* Ivan N. Ianakiev, Jun 18 2015 *)
fQ[n_]:=StringContainsQ[ToString[n*(n+1)/2-DivisorSigma[1,n]],ToString[DivisorSigma[1,n]]];Select[Range[10^5],fQ[#]&] (* much faster *) (* Ivan N. Ianakiev, Apr 02 2022 *)

Extensions

a(16)-a(32) from Giovanni Resta, Jun 08 2015