

A241501


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


1



167564622641, 174977122641, 175543159858, 175543162247, 183477122641, 183518142444, 191500000000, 2779888721787, 2784986175699, 212148288981849, 212148288982006, 315131893491390, 321400000000000, 417586822240846, 417586822241003, 418112649991390
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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!/(n2)!/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^nb1, if (hammingweight(j) == (nb2), 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 A105295 A288262
Adjacent sequences: A241498 A241499 A241500 * A241502 A241503 A241504


KEYWORD

nonn,base


AUTHOR

Anthony Sand, Apr 24 2014


STATUS

approved



