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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn,base
AUTHOR
Anthony Sand, Apr 24 2014
STATUS
approved