A067013 -id:A067013 - cp's OEIS frontend

A067012 Absolute composites: every permutation of digits (dropping any leading zeros) is a composite number.

4, 6, 8, 9, 12, 15, 18, 21, 22, 24, 25, 26, 27, 28, 33, 36, 39, 40, 42, 44, 45, 46, 48, 49, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 72, 75, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 93, 94, 96, 99, 102, 105, 108, 111, 114, 116, 117, 120, 122, 123

Offset: 1

Lior Manor, Dec 26 2001

			18 is a term since it is composite and the permutation 81 is composite too.

T. D. Noe, Table of n, a(n) for n = 1..10000

Subsequence of A067013.

t={}; Do[l1=Table[FromDigits[k], {k,Permutations[IntegerDigits[n]]}]; If[Select[l1,PrimeQ] == {} && FreeQ[l1,1] == True, AppendTo[t,n]],{n,123}]; t  (* Jayanta Basu, May 03 2013  *)

A096600 Numbers such that in decimal representation all permutations of digits are nonsquares.

Original entry on oeis.org

2, 3, 5, 6, 7, 8, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 50, 51, 53, 54, 55, 56, 57, 58, 59, 60, 62, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87

Offset: 1

Reinhard Zumkeller, Jun 29 2004

A062892(a(n)) = 0.

			134=2*67, 143=11*13, 314=2*157, 341=11*31, 413=7*59 and 431=A000040(83), therefore 134, 143, 314, 341, 413 and 431 are terms.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A007937, A096599, A000037, A067013.

Select[Range[100],NoneTrue[Sqrt[#]&/@(FromDigits/@Permutations[IntegerDigits[ #]]),IntegerQ]&] (* Harvey P. Dale, Dec 04 2022 *)

A228096 Numbers consisting of only odd digits such that no permutation of its digits yields a prime.

Original entry on oeis.org

1, 9, 15, 33, 39, 51, 55, 57, 75, 77, 93, 99, 111, 117, 135, 153, 155, 159, 171, 177, 195, 315, 333, 339, 351, 355, 357, 375, 393, 399, 513, 515, 519, 531, 535, 537, 551, 553, 555, 559, 573, 579, 591, 595, 597, 711, 717, 735, 753, 759, 771, 777, 795

Offset: 1

Jayanta Basu, Aug 10 2013

Apart from the first term, A061810 is a subsequence. Conjecture: a(n) ~ A061810(n). - Charles R Greathouse IV, Feb 15 2017

			51 is a member since it consists of only odd digits and both 15 and 51 are composites.

Jayanta Basu, Table of n, a(n) for n = 1..1000

Subsequence of A067013.

Cf. A067013, A061810.

Select[Range[800], And @@ OddQ[x = IntegerDigits[#]] && Count[FromDigits /@ Permutations[x], _?PrimeQ] == 0 &]
Table[FromDigits/@Select[Tuples[Range[1,9,2],n],NoneTrue[FromDigits/@ Permutations[#],PrimeQ]&],{n,3}]//Flatten (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 09 2019 *)

A248010 Non-primatic permutable numbers: All permutations of the number's digits except the ones resulting in leading zeros are nonprimes.

Original entry on oeis.org

1, 4, 6, 8, 9, 10, 12, 15, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 33, 36, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 93, 94, 96, 99, 100, 102, 105, 108, 111, 114, 116, 117, 120, 122, 123, 126, 129, 132, 135, 138, 141, 144, 147

Offset: 1

Andreas Boe, Sep 29 2014

This sequence differs slightly from "absolute composite numbers". 30 is not an absolute composite since 03 is counted as a prime, but in this sequence permutations with leading zeros are disqualified as viable permutations.

			7000 qualifies since it is a composite and the only allowed permutation of its four digits.

Andreas Boe, Table of n, a(n) for n = 1..10000

Absolute composites: A067012, A067013.
Monoprimatic permutable numbers: A245808.
Biprimatic permutable numbers: A246043.

A225438 Odd numbers such that no permutation of its digits yields a prime.

Original entry on oeis.org

1, 9, 15, 21, 25, 27, 33, 39, 45, 49, 51, 55, 57, 63, 65, 69, 75, 77, 81, 85, 87, 93, 99, 105, 111, 117, 123, 129, 135, 141, 147, 153, 155, 159, 161, 165, 171, 177, 183, 185, 187, 189, 195, 201, 205, 207, 213, 219, 221, 225, 231, 237, 243, 245, 247, 249

Offset: 1

Jayanta Basu, May 08 2013

Subset of A067013.

			105 is a member since none of 105, 150, 15, 51, 510, 501 is a prime.

Cf. A067013.

t={}; Do[If[Length[Select[Table[FromDigits[k], {k,Permutations[IntegerDigits[n]]}],PrimeQ]]==0, AppendTo[t,n]], {n,1,250,2}]; t

cp's OEIS Frontend

A067012 Absolute composites: every permutation of digits (dropping any leading zeros) is a composite number.

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A096600 Numbers such that in decimal representation all permutations of digits are nonsquares.

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A228096 Numbers consisting of only odd digits such that no permutation of its digits yields a prime.

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A248010 Non-primatic permutable numbers: All permutations of the number's digits except the ones resulting in leading zeros are nonprimes.

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A225438 Odd numbers such that no permutation of its digits yields a prime.

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