cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A202259 Right-truncatable nonprimes: every prefix is nonprime number.

Original entry on oeis.org

0, 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 40, 42, 44, 45, 46, 48, 49, 60, 62, 63, 64, 65, 66, 68, 69, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 120, 121, 122, 123, 124, 125, 126, 128, 129, 140, 141, 142
Offset: 1

Views

Author

Jaroslav Krizek, Dec 25 2011

Keywords

Comments

Supersequence of A202260, A202265. - Barry Carter, Sep 16 2016

Links

Crossrefs

Cf. A012883 (right-truncatable noncomposites), A024770 (right-truncatable primes), A202260 (right-truncatable composites).

Programs

  • Maple
    filter:= proc(n) option remember; not isprime(n) and procname(floor(n/10)) end proc:
for i from 0 to 9 do filter(i):= not isprime(i) od:
select(filter, [$0..1000]); # Robert Israel, Nov 01 2016

A202262 Composite numbers in which all substrings are composite.

Original entry on oeis.org

4, 6, 8, 9, 44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 94, 96, 98, 99, 444, 446, 448, 464, 466, 468, 469, 484, 486, 488, 494, 496, 498, 644, 646, 648, 649, 664, 666, 668, 669, 684, 686, 688, 694, 696, 698, 699, 844, 846, 848, 849, 864, 866, 868, 869, 884, 886
Offset: 1

Views

Author

Jaroslav Krizek, Dec 25 2011

Keywords

Comments

Subsequence of A062115, A202260, A029581.
Supersequence of A202265.
This is a 10-automatic sequence, see A071062. - Charles R Greathouse IV, Jan 01 2012

Links

Crossrefs

Cf. A085823 (primes in which all substrings are primes), A068669 (noncomposite numbers in which all substrings are noncomposite), A062115 (nonprimes in which all substrings are nonprimes).
Cf. A010051.

Programs

  • Mathematica
    sub[n_] := Block[{d = IntegerDigits[n]}, Union@ Reap[ Do[Sow@ FromDigits@ Take[d, {i, j}], {j, Length@ d}, {i, j}]][[2, 1]]]; Select[ Range@ 900, Union[{4, 6, 8, 9}, IntegerDigits[#]] == {4, 6, 8, 9} && AllTrue[sub[#], CompositeQ] &] (* Giovanni Resta, Dec 20 2019 *)
  • PARI
    See Links section.

Extensions

Data corrected by Reinhard Zumkeller, May 05 2012
Data corrected by Rémy Sigrist, Dec 19 2019
Incorrect Haskell program deleted by M. F. Hasler, Dec 20 2019

A254750 Numbers such that, in base 10, all their proper prefixes and suffixes represent composites.

Original entry on oeis.org

44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 89, 94, 96, 98, 99, 404, 406, 408, 409, 424, 426, 428, 444, 446, 448, 449, 454, 456, 458, 464, 466, 468, 469, 484, 486, 488, 494, 496, 498, 499, 604, 606, 608, 609, 624, 626, 628, 634, 636, 638
Offset: 1

Views

Author

Stanislav Sykora, Feb 15 2015

Keywords

Comments

A proper prefix (or suffix) of a number m is one which is neither void, nor identical to m.
Alternative definition: Slicing the decimal expansion of a(n) in any way into two nonempty parts, each part represents a composite number.
The list is infinite because any string of two or more digits selected from {4,6,8} represents a member.
Each member a(n) starts, as well as ends, with one of the digits {4,6,8,9}.
Every proper prefix of each member a(n) is a member of A202260, and every proper suffix is a member of A254755.
The sequence is a union of A254752 and A254754.

Examples

			6 is not a member because its expansion cannot be sliced in two.
638 is a member because (6, 38, 63, and 8) are all composites.

Links

Crossrefs

Cf. A202260, A254751, A254752, A254753, A254754, A254755.

Programs

  • PARI
    isComposite(n) = (n>2)&&(!isprime(n));
slicesIntoComposites(n,b=10) = {my(k=b);if(n0,if(!isComposite(n\k)||!isComposite(n%k),return(0););k*=b);return(1);}

A254754 Prime numbers such that, in base 10, all their proper prefixes and suffixes represent composites.

Original entry on oeis.org

89, 409, 449, 499, 809, 4049, 4549, 4649, 4909, 4969, 6299, 6469, 6869, 6899, 6949, 8009, 8039, 8069, 8209, 8609, 8669, 8699, 8849, 9049, 9209, 9649, 9949, 40009, 40099, 40609, 40639, 40699, 40849, 42209, 42649, 44249, 44699, 45949, 46049, 46099
Offset: 1

Views

Author

Stanislav Sykora, Feb 15 2015

Keywords

Comments

A proper prefix (or suffix) of a number m is one which is neither void, nor identical to m.
Alternative definition: Slice the decimal expansion of the prime number a(n) in any way into two nonempty parts; then both parts represent a composite number.
This sequence is a subset of A254750. Each member a(n) must start with one of the digits {4,6,8,9} and end with 9.
Every proper prefix of each member a(n) is a member of A202260, and every proper suffix is a member of A254755.
These numbers are rare and tend to become rarer with increasing n, but the sequence does not seem to terminate (for example, 4*10^28 + 9 is a member).

Examples

			7 is not a member because its expansion cannot be sliced in two.
The prime 4969 is a member because it is a prime and the slices (4, 969, 49, 69, 496, and 9) are all composites.

Links

Crossrefs

Cf. A202260, A254750, A254751, A254752, A254753, A254755.

Programs

  • Mathematica
    Select[Prime[Range[5,5000]],AllTrue[Flatten[Table[FromDigits/@TakeDrop[IntegerDigits[#],n],{n,IntegerLength[ #]-1}]],CompositeQ]&] (* Harvey P. Dale, Sep 22 2024 *)
  • PARI
    isComposite(n) = (n>2)&&(!isprime(n));
slicesIntoComposites(n,b=10) = {my(k=b);if(n0,if(!isComposite(n\k)||!isComposite(n%k),return(0););k*=b);return(1);}
isPrimeSlicingIntoComposites(n,b=10) = isprime(n) && slicesIntoComposites(n,b);

A254752 Composite numbers such that, in base 10, all their proper prefixes and suffixes represent composites.

Original entry on oeis.org

44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 94, 96, 98, 99, 404, 406, 408, 424, 426, 428, 444, 446, 448, 454, 456, 458, 464, 466, 468, 469, 484, 486, 488, 494, 496, 498, 604, 606, 608, 609, 624, 626, 628, 634, 636, 638, 639, 644, 646, 648, 649, 654, 656, 658, 664, 666, 668, 669, 684, 686, 688, 694, 696, 698, 699, 804, 806, 808, 814, 816, 818, 824, 826, 828
Offset: 1

Views

Author

Stanislav Sykora, Feb 15 2015

Keywords

Comments

A proper prefix (or suffix) of a number m is one which is neither void, nor identical to m.
Alternative definition: Slicing the decimal expansion of the composite number a(n) in any way into two nonempty parts, each part represents a composite number.
This list is infinite because any string of two or more digits selected from {4,6,8} is a member.
It is a subsequence of A254750 and shares with it these properties: Each member of a(n) must start, as well as end, with one of the digits {4,6,8,9}. Every proper prefix of each member a(n) is a member of A202260, and every proper suffix is a member of A254755.

Examples

			6 is not a member because its expansion cannot be sliced in two.
The composite 469 is a member because it is a composite and the slices (4, 69, 46, and 9) are all composites.

Links

Crossrefs

Cf. A202260, A254750, A254751, A254753, A254754, A254755.

Programs

  • PARI
    isComposite(n) = (n>2)&&(!isprime(n));
slicesIntoComposites(n,b=10) = {my(k=b);if(n0,if(!isComposite(n\k)||!isComposite(n%k),return(0););k*=b);return(1);}
isCompositeSlicingIntoComposites(n,b=10) = isComposite(n) && slicesIntoComposites(n,b);

A254755 Left-truncatable composites: every decimal suffix is a composite number.

Original entry on oeis.org

4, 6, 8, 9, 14, 16, 18, 24, 26, 28, 34, 36, 38, 39, 44, 46, 48, 49, 54, 56, 58, 64, 66, 68, 69, 74, 76, 78, 84, 86, 88, 94, 96, 98, 99, 104, 106, 108, 114, 116, 118, 124, 126, 128, 134, 136, 138, 144, 146, 148, 154, 156, 158, 164, 166, 168
Offset: 1

Views

Author

Stanislav Sykora, Feb 15 2015

Keywords

Examples

			549 is a member because 549, 49, and 9 are all composites.

Links

Crossrefs

Cf. A103443 (left-truncatable primes), A202260 (right-truncatable composites), A254750.

Programs

  • PARI
    isComposite(n) = (n>2)&&(!isprime(n));
isLeftTruncatableComposite(n,b=10) = {my(k=b);if(!isComposite(n),return(0););while(n\k>0,if(!isComposite(n%k),return(0););k*=b);return(1);}
Showing 1-6 of 6 results.

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