A237424 - OEIS

A237424

Numbers of the form (10^a + 10^b + 1)/3.

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

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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

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

(Magma)

A052216:=[10^(n-1) + 10^(k-1): k in [1..n], n in [1..100]];

A237424:= func< n | (A052216[n]+1)/3 >;

[A237424(n): n in [1..100]]; // G. C. Greubel, Feb 22 2024

(SageMath)

A052216=flatten([[10^(n-1) + 10^(k-1) for k in range(1, n+1)] for n in range(1, 101)])

def A237424(n): return (A052216[n-1]+1)//3

[A237424(n) for n in range(1, 101)] # G. C. Greubel, Feb 22 2024

CROSSREFS

Cf. A028819, A028820, A028821, A052216, A067275, A093137, A234841, A254143.

Sequence in context: A004031 A243863 A153062 * A143547 A149090 A103059

Adjacent sequences: A237421 A237422 A237423 * A237425 A237426 A237427