A241501 Numbers n such that the sum of all numbers formed by deleting two digits from n is equal to n.

167564622641, 174977122641, 175543159858, 175543162247, 183477122641, 183518142444, 191500000000, 2779888721787, 2784986175699, 212148288981849, 212148288982006, 315131893491390, 321400000000000, 417586822240846, 417586822241003, 418112649991390

Offset: 1

Author

Anthony Sand, Apr 24 2014

Keywords

• nonn
• base

Examples

			Sum(650000000000000) (15 digits) = 6000000000000 x 13 + 5000000000000 x 13 + 6500000000000 x (78 = 13C2) + 0.
		

Links

• Anthony Sand, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A131639 (n equal to sum of all numbers formed by deleting one digit from n).

Programs

PARI

padbin(n, len) = {b = binary(n); while(length(b) < len, b = concat(0, b);); b;}
isok(n) = {d = digits(n); nb = #d; s = 0; for (j=1, 2^nb-1, if (hammingweight(j) == (nb-2), b = padbin(j, nb); nd = []; k = 1; for (i=1, nb, if (b[i], nd = concat(nd, d[k])); k++;); s += subst(Pol(nd), x, 10););); s == n;} \\ Michel Marcus, Apr 25 2014

Formula

For a number with n digits there are nC2 = n!/(n-2)!/2! substrings generated by removing two digits from the original number. So for 12345, these are 345, 245, 235, 234, 145, 135, 134, 125, 124, 123. Sum(x) is defined as the sum of these substrings for a number x and the sequence above is those numbers such that sum(x) = x.