A255968 Numbers k such that antisigma(k) contains k as a substring.

24, 57, 204, 411, 559, 2004, 2440, 3935, 6616, 8640, 20004, 34939, 55827, 61009, 64599, 79747, 87113, 87269, 96513, 481557, 621265, 647532, 702893, 704682, 797465, 2000004, 2385120, 4066960, 4566616, 8984375, 20000004, 54636003, 65061605

Offset: 1

Author

Paolo P. Lava, Mar 12 2015

Keywords

• nonn
• base

Comments

Any number of the form 20...04, with a number of consecutive zeros not equal to 6*k+4 (with k = 0, 1, 2, 3,...), appears to belong to the sequence.

Examples

			antisigma(24) = (24*25) / 2 - sigma(24) = 300 - 60 = 240 and 24 is a substring;
antisigma(57) = (57*58) / 2 - sigma(57) =  1653 - 80 = 1573 and 57 is a substring.
		

Crossrefs

Cf. A024816.

Programs

Maple

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

Mathematica

Select[Range[800000],SequenceCount[IntegerDigits[(#(#+1))/2-DivisorSigma[1,#]],IntegerDigits[#]]>0&] (* The program generates the first 25 terms of the sequence. *) (* Harvey P. Dale, Jun 23 2025 *)

Extensions

a(28)-a(33) from Robert Israel, Dec 20 2024