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

1,1

Links

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

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.

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A271819 A304235 A233503 * A197633 A339122 A105295

Adjacent sequences: A241498 A241499 A241500 * A241502 A241503 A241504

Keyword

nonn,base

Author

Anthony Sand, Apr 24 2014

Status

approved