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 A166323 Numbers in which all the digits are larger than the arithmetic mean of their two neighbors. 1
 110, 120, 121, 122, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 145, 146, 150, 151, 152, 153, 154, 155, 156, 157, 158, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Last term of the sequence is a(3569) = 36899863. The criterion on the arithmetic mean is only applied to the digits which have two neighbors, that is, not to the first and last digit. If we look at the isolated digits d(i) of n = sum_i d(i)*10^(i-1) as function values defined over the regular abscissas of i=1,2,..., the criterion is equivalent to saying that the discrete approximation of the second derivative of the function is negative where defined, that is, the function is everywhere concave. From Rick L. Shepherd, Feb 20 2013: (Start) There are 405, 925, 1149, 781, 271, 38 terms of digit lengths 3 through 8, respectively, where 110, 1220, 13320, 134430, 1466530, 14677640 are the least and 998, 9986, 99863, 899863, 6899863, 36899863 are the greatest. This sequence has the property that any three-digit-or-larger substring of a term's digit string is a term. Hence the fact that there is no nine-digit term proves there are no terms with even more digits. The sequence of terms that are not substrings of greater terms begins 110, 120, 121, 130, 131, 140, 141, 142, 150, 151, 152, 160, 161, 162, 163, 170, .... (End) LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..3569 (full sequence) MAPLE isA166323 := proc(n) local d, k: d:=convert(n, base, 10): for k from 2 to nops(d)-1 do if(2*d[k]<=d[k-1]+d[k+1])then return NULL: fi: od: return n: end: seq(isA166323(n), n=100..200); # Nathaniel Johnston, Jun 17 2011 MATHEMATICA dlamQ[n_]:=And@@(#[[2]]>(#[[1]]+#[[3]])/2&/@Partition[IntegerDigits[n], 3, 1]) Select[Range[100, 200], dlamQ] (* Harvey P. Dale, Feb 17 2011 *) CROSSREFS Cf. A135642. [R. J. Mathar, Oct 14 2009] Sequence in context: A171236 A279421 A135642 * A194429 A320121 A084042 Adjacent sequences: A166320 A166321 A166322 * A166324 A166325 A166326 KEYWORD fini,full,nonn,base,easy AUTHOR Claudio Meller, Oct 11 2009 EXTENSIONS keyword:base and most of the comment added by R. J. Mathar, Oct 14 2009 STATUS approved

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Last modified September 9 16:11 EDT 2024. Contains 375765 sequences. (Running on oeis4.)