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 A237424 Numbers of the form (10^a + 10^b + 1)/3. 8
 1, 4, 7, 34, 37, 67, 334, 337, 367, 667, 3334, 3337, 3367, 3667, 6667, 33334, 33337, 33367, 33667, 36667, 66667, 333334, 333337, 333367, 333667, 336667, 366667, 666667, 3333334, 3333337, 3333367, 3333667, 3336667 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Has the property that the product of any two (not necessarily distinct) terms has digits in nondecreasing order. Conjecture: This sequence is in a sense the maximally dense sequence with this nondecreasing products property. That is, it appears that every maximal sequence is either (i) A237424, (ii) a finite set of "extra" terms plus A237424 restricted to b=0 (which is A093137), or (iii) a finite set of "extra" terms plus A237424 restricted to a=b (which is A067275). (There might be one more case, not yet identified.) - David Applegate, Feb 12 2014 See A254143 and link for products a(i)*a(j) in natural order. - Reinhard Zumkeller, Jan 28 2015 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (first 1035 terms from Robert G. Wilson v) Reinhard Zumkeller, First 10000 products of any two terms of A237424 FORMULA a(n) = (A052216(n)+1)/3. - Reinhard Zumkeller, Jan 28 2015 EXAMPLE 36667*66667 = 2444478889. MATHEMATICA Union@ Flatten@ Table[(10^a + 10^b + 1)/3, {a, 0, 8}, {b, a, 8}] (* Robert G. Wilson v, Jan 26 2015 *) (10^#[[1]]+10^#[[2]]+1)/3&/@Tuples[Range[0, 8], 2]//Union (* Harvey P. Dale, May 28 2019 *) PROG (Haskell) a237424 = flip div 3 . (+ 1) . a052216 -- Reinhard Zumkeller, Jan 28 2015 (PARI) list(lim)=my(v=List(), a, t); while(1, for(b=0, a, t=(10^a+10^b+1)/3; if(t>lim, return(Set(v))); listput(v, t)); a++) \\ Charles R Greathouse IV, May 13 2015 CROSSREFS Cf. A028819, A028820, A028821, A234841, A093137, A067275, A254143, A052216. Sequence in context: A004031 A243863 A153062 * A143547 A149090 A103059 Adjacent sequences:  A237421 A237422 A237423 * A237425 A237426 A237427 KEYWORD nonn AUTHOR Ahmad J. Masad, Feb 07 2014 EXTENSIONS Edited by David Applegate, Feb 07 2014 STATUS approved

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Last modified September 23 09:03 EDT 2020. Contains 337298 sequences. (Running on oeis4.)