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 1-7 of 7 results.

A086923 Primes arising in A086920, or 0 if A086920(n) = 0.

Original entry on oeis.org

11, 331, 2221, 33331, 333331, 3333331, 33333331, 30303030303030301, 6666666661, 44444444441, 555555555551, 5555555555551, 252525252525252525252525251, 42424242424242424242424242421, 1717171717171717171717171717171
Offset: 1

Views

Author

Amarnath Murthy, Sep 18 2003

Keywords

Crossrefs

Cf. A086920, A087604, A087605, A087606, A087607, A087608, A087609.

Extensions

More terms from David Wasserman, Apr 12 2005

A087604 Smallest k such that n times concatenation of k with itself followed by a 3 is a prime, or 0 if no such number exists.

Original entry on oeis.org

1, 1, 0, 1, 4, 0, 2, 1, 0, 1, 4, 0, 37, 7, 0, 17, 149, 0, 185, 7, 0, 73, 1, 0, 5, 47, 0, 38, 4, 0, 4, 133, 0, 52, 2, 0, 194, 46, 0, 37, 29, 0, 29, 25, 0, 19, 14, 0, 74, 8, 0, 19, 20, 0, 442, 83, 0, 358, 211, 0, 16, 298, 0, 260, 5, 0, 305, 71, 0, 8, 323, 0, 5, 109, 0, 8, 68, 0, 767, 367
Offset: 1

Views

Author

Amarnath Murthy, Sep 18 2003

Keywords

Comments

Trivially a(3n) = 0. Conjecture: no other term is zero.
Either a(13)=0 or a(13)>36. This sequence contains no positive multiples of 3. If a(m) is of the form bbb...b (repeated k times) then a(km) <= b. - Sam Alexander, Oct 20 2003

Examples

			a(5) = 4 as 444443 is a prime. but 111113,222223,333333 are not.

Crossrefs

Cf. A086920, A087605, A087606, A087607, A087608, A087609, A087610.

Extensions

More terms from Sam Alexander, Oct 20 2003
More terms from Ray G. Opao, Apr 15 2004
More terms from David Wasserman, Jun 16 2005

A087605 Smallest k such that n times concatenation of k with itself followed by a 7 is a prime, or 0 if no such number exists.

Original entry on oeis.org

1, 2, 1, 1, 3, 100005, 1, 2, 4, 6, 8, 100010, 19, 2, 215, 9, 60, 100041, 4, 66, 5, 1, 41, 100061, 4, 15, 2, 1, 195, 100055, 61, 1061, 143, 12, 72, 100127, 19, 60, 1, 6, 125, 0, 45, 1305, 3, 39, 27, 100269, 72, 95, 136, 1123, 50, 100193, 52, 1056, 176, 1536, 66
Offset: 1

Views

Author

Amarnath Murthy, Sep 18 2003

Keywords

Comments

a(42n)=0, but all other terms are probably nonzero. For n a multiple of 42, (10^(l*n)-1)/(10^l-1)*10+7 is divisible by 7 for any l. - Max Alekseyev, Feb 11 2005

Examples

			a(5) = 3 as 333337 is a prime but 111117 and 222227 are not.

Crossrefs

Cf. A086920, A087604, A087606, A087607, A087608, A087609, A087610.

Programs

  • PARI
    { a(n) = if(n%42==0,return(0)); for(l=1,10^6, if(valuation(10^(l*n)-1,7)==valuation(10^l-1,7), for(k=10^(l-1),10^l-1, if(isprime(k*(10^(l*n)-1)/(10^l-1)*10+7), return(k) ) ) ) ) } (Alekseyev)

Formula

Minimal k such that k*(10^(l*n)-1)/(10^l-1)*10+7 is prime, where l is the length of k; and 0 if no such prime exists. - Max Alekseyev, Feb 11 2005

Extensions

Corrected and extended by Max Alekseyev, Feb 11 2005

A087606 Smallest k such that n times concatenation of k with itself followed by a 9 is a prime, or 0 if no such number exists.

Original entry on oeis.org

1, 2, 0, 1, 1, 0, 1, 11, 0, 64, 5, 0, 2, 31, 0, 1, 5, 0, 10, 65, 0, 41, 212, 0, 5, 79, 0, 41, 160, 0, 5, 94, 0, 8, 82, 0, 23, 43, 0, 40, 26, 0, 391, 119, 0, 212, 4, 0, 1, 160, 0, 134, 28, 0, 208, 50, 0, 248, 35, 0, 113, 43, 0, 79, 7, 0, 70, 170, 0, 64, 94, 0, 19, 86, 0, 10, 118, 0, 34, 98
Offset: 1

Views

Author

Amarnath Murthy, Sep 18 2003

Keywords

Comments

Conjecture: a(3n) = 0. No other term is zero.
a(3n)=0: consider the sum of the digits modulo 3. For the same reason, if a(m) is divisible by 3 then a(m)=0. - Sam Alexander, Nov 15 2003

Examples

			a(2) = 2 as 229 is a prime. but 119 is not.

Links

Crossrefs

Cf. A086920, A087604, A087605, A087607, A087608, A087609, A087610.

Programs

  • Mathematica
    s[b_]:=(v={};l=Length[b];Do[v=Join[v, IntegerDigits[b[[k]]]], {k, l}];v); a[n_]:=If[Mod[n, 3]!= 0, (For[m = 1, ! PrimeQ[10*FromDigits[s[Table[m, {n}]]] +9], m++ ];m), 0]; Table[a[n], {n, 90}] (Firoozbakht)

Extensions

More terms from Sam Alexander, Nov 15 2003
More terms from Farideh Firoozbakht, Feb 04 2005

A087607 Primes arising in A087606, or 0 if A087606(k) = 0.

Original entry on oeis.org

19, 229, 0, 11119, 111119, 0, 11111119, 11111111111111119, 0, 646464646464646464649, 555555555559, 0, 22222222222229, 31313131313131313131313131319, 0, 11111111111111119, 555555555555555559, 0, 101010101010101010101010101010101010109
Offset: 1

Views

Author

Amarnath Murthy, Sep 18 2003

Keywords

Crossrefs

Cf. A086920, A087604, A087605, A087606, A087608, A087609, A087610.

Extensions

More terms from Michel Marcus, Feb 28 2014

A087608 Primes arising in A087605, or 0 if A087605(n) = 0.

Original entry on oeis.org

17, 227, 1117, 11117, 333337, 1000051000051000051000051000051000057, 11111117, 222222227, 4444444447, 66666666667, 888888888887, 1000101000101000101000101000101000101000101000101000101000101000101000107, 191919191919191919191919197, 222222222222227
Offset: 1

Views

Author

Amarnath Murthy, Sep 18 2003

Keywords

Crossrefs

Cf. A086920, A087604, A087605, A087606, A087607, A087609, A087610.

Extensions

a(6) corrected according to A087605(6) and more terms from Michel Marcus, Feb 28 2014

A087609 Primes arising in A087604, or 0 if A087604(n) = 0.

Original entry on oeis.org

13, 113, 0, 11113, 444443, 0, 22222223, 111111113, 0, 11111111113, 444444444443, 0, 373737373737373737373737373, 777777777777773, 0, 171717171717171717171717171717173, 1491491491491491491491491491491491491491491491491493, 0, 1851851851851851851851851851851851851851851851851851851853
Offset: 1

Views

Author

Amarnath Murthy, Sep 18 2003

Keywords

Comments

Either a(13)=0 or a(13) > 363636363636363636363636363. - Sam Alexander, Oct 20 2003

Crossrefs

Cf. A086920, A087604, A087605, A087606, A087607, A087608, A087610.

Extensions

More terms from Sam Alexander, Oct 20 2003
More terms from David Wasserman, Jun 16 2005
Showing 1-7 of 7 results.

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