A198382 -id:A198382 - cp's OEIS frontend

A195993 Numbers n such that 90n + 73 is prime.

0, 1, 4, 5, 6, 9, 11, 12, 15, 18, 19, 20, 22, 23, 27, 28, 29, 32, 36, 39, 40, 42, 43, 49, 51, 54, 55, 56, 61, 62, 63, 65, 70, 72, 74, 75, 85, 88, 91, 92, 93, 95, 96, 97, 98, 103, 104, 106, 109, 110, 113, 114, 116, 127, 128, 131

Offset: 1

J. W. Helkenberg, Oct 27 2011

This sequence results from the propagation (addition) of 12 Fibonacci-like sequences; this sequence contains (recovers) all digital root 1 and last digit 3 prime numbers.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382.

A142326 := proc(n)
        option remember;
        if n = 1 then
                73 ;
        else
                a := nextprime(procname(n-1)) ;
                while (a mod 45) <> 28 do
                        a := nextprime(a) ;
                end do;
                return a;
        end if;
end proc:
A195993 := proc(n)
        (A142326(n)-73)/90 ;
end proc:
seq(A195993(n),n=1..80) ; # R. J. Mathar, Oct 31 2011

Select[Range[0,200],PrimeQ[90#+73]&] (* Harvey P. Dale, May 05 2014 *)

is(n)=isprime(90*n+73) \\ Charles R Greathouse IV, Apr 25 2016

a(n) = (A142326(n)-73)/90.

A196000 Numbers k such that 90*k + 19 is prime.

Original entry on oeis.org

0, 1, 2, 4, 8, 9, 10, 11, 14, 16, 17, 22, 23, 24, 25, 28, 30, 34, 35, 36, 39, 41, 43, 46, 48, 50, 53, 55, 56, 60, 63, 64, 65, 69, 74, 77, 78, 79, 80, 81, 83, 85, 86, 91, 93, 98, 99, 101, 102, 107, 108, 109, 111, 112, 115, 116

Offset: 1

J. W. Helkenberg, Oct 27 2011

A142322 is a digital root 1 and last digit 9 preserving sequence.

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A195953, A181732, A198382.

A142322 := proc(n)
        option remember;
        if n = 1 then
                19 ;
        else
                a := nextprime(procname(n-1)) ;
                while (a mod 45) <> 19 do
                        a := nextprime(a) ;
                end do;
                return a;
        end if;
end proc:
A196000 := proc(n)
        (A142322(n)-19)/90 ;
end proc:
seq(A196000(n),n=1..80) ; # R. J. Mathar, Oct 31 2011

Select[Range[0, 120], PrimeQ[90 # + 19] &] (* Ivan Neretin, Apr 27 2017 *)

is(n)=isprime(90*n+19) \\ Charles R Greathouse IV, Apr 25 2016

a(n) = (A142322(n) - 19)/90.

A196007 Numbers n such that 90n + 83 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 10, 12, 15, 16, 17, 21, 22, 23, 24, 25, 26, 29, 32, 36, 37, 39, 42, 45, 49, 50, 51, 54, 58, 59, 60, 61, 64, 67, 68, 71, 72, 73, 75, 77, 78, 79, 80, 84, 86, 89, 91, 92, 94, 101, 105, 106, 108, 112, 113, 114, 115, 117, 120

Offset: 1

J. W. Helkenberg, Oct 27 2011

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A196000, A198382, A181732, A195993. These are digital root and last digit preserving sequences.

A142332 := proc(n)
        option remember;
        if n = 1 then
                83 ;
        else
                a := nextprime(procname(n-1)) ;
                while (a mod 45) <> 38 do
                        a := nextprime(a) ;
                end do;
                return a;
        end if;
end proc:
A196007 := proc(n)
        (A142332(n)-83)/90 ;
end proc:
seq(A196007(n),n=1..80) ; # R. J. Mathar, Oct 31 2011

Select[Range[0, 120], PrimeQ[90 # + 83] &] (* Ivan Neretin, May 02 2017 *)

is(n)=isprime(90*n+83) \\ Charles R Greathouse IV, Jul 12 2016

a(n) = (A142332(n)-83)/90.

A201734 Numbers n such that 90*n + 47 is prime.

Original entry on oeis.org

0, 1, 2, 3, 6, 7, 9, 10, 13, 14, 16, 18, 20, 22, 24, 25, 27, 29, 31, 32, 38, 39, 43, 44, 49, 50, 51, 53, 56, 63, 64, 65, 66, 69, 77, 80, 83, 84, 87, 90, 91, 95, 98, 101, 102, 105, 106, 107, 108, 109, 111, 116, 118, 120, 121, 122, 123, 129, 132, 134, 135, 137

Offset: 1

J. W. Helkenberg, Dec 04 2011

A reverse reading of A142313; all entries of A142313 have digital root 2 and last digit 7.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007.

[n: n in [0..200] | IsPrime(90*n+47)]; // Vincenzo Librandi, Dec 11 2011

for n from 0 to 240 do
    p := 90*n+47 ;
    if isprime(p) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Dec 05 2011

Select[Range[0,400],PrimeQ[90 #+47]&] (* Vincenzo Librandi, Dec 11 2011 *)

is(n)=isprime(90*n+47) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A142313(n)-47)/90.

A201739 Numbers n such that 90*n + 29 is prime.

Original entry on oeis.org

0, 4, 5, 6, 7, 9, 10, 11, 12, 14, 17, 23, 27, 28, 30, 31, 32, 33, 34, 37, 38, 39, 41, 44, 45, 47, 48, 53, 54, 61, 65, 70, 73, 74, 75, 76, 77, 80, 83, 84, 88, 89, 91, 96, 98, 100, 102, 105, 108, 109, 110, 114, 117, 119, 125, 126, 128, 132, 136, 139, 142, 143

Offset: 1

J. W. Helkenberg, Dec 04 2011

This sequence was generated by adding 12 Fibonacci-like sequences. Looking at the format 90n+29 modulo 9 and modulo 10 we see that all entries of A142327 have digital root 2 and last digit 9. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201734.

[n: n in [0..200] | IsPrime(90*n+29)]; // Vincenzo Librandi, Dec 11 2011

for n from 0 to 240 do
    p := 90*n+29 ;
    if isprime(p) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Dec 05 2011

Select[Range[0,400],PrimeQ[90 #+29]&] (* Vincenzo Librandi, Dec 11 2011 *)

forstep(n=29,1e4,90,if(isprime(n),print1(n\90", "))) \\ Charles R Greathouse IV, Dec 05 2011

a(n) = (A142327(n) - 29)/90.

A201804 Numbers k such that 90*k + 11 is prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 7, 9, 10, 12, 13, 15, 16, 19, 20, 21, 23, 26, 27, 28, 29, 30, 31, 36, 41, 43, 47, 49, 52, 54, 56, 58, 61, 62, 65, 68, 69, 70, 72, 73, 75, 79, 80, 83, 87, 90, 92, 97, 98, 100, 103, 104, 105, 106, 112, 113, 114, 118, 124, 125

Offset: 1

J. W. Helkenberg, Dec 05 2011

This sequence was generated by adding 12 Fibonacci-like sequences. Looking at 90*k+11 modulo 9 and modulo 10 we see that all entries of A142317 have digital root 2 and last digit 1. (Reverting the process is an application of the Chinese remainder theorem)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734.

[n: n in [0..200] | IsPrime(90*n+11)]; // Vincenzo Librandi, Dec 11 2011

Select[Range[0,40000],PrimeQ[90 #+11]&] (* Vincenzo Librandi, Dec 11 2011 *)

a(24)-a(59) from Vincenzo Librandi, Dec 11 2011

A201816 Numbers k such that 90*k + 13 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 8, 9, 12, 16, 17, 19, 22, 23, 30, 31, 35, 36, 37, 38, 40, 42, 46, 47, 49, 50, 51, 53, 58, 59, 60, 61, 63, 66, 67, 68, 74, 75, 80, 82, 84, 86, 88, 92, 95, 99, 100, 101, 103, 105, 107, 108, 112, 114, 116, 119, 121, 122, 123, 124, 126, 127

Offset: 1

J. W. Helkenberg, Dec 05 2011

Looking at the format 90*k+13 modulo 9 and modulo 10 we see that all entries of A142318 have digital root 4 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804.

[n: n in [0..200] | IsPrime(90*n+13)]; // Vincenzo Librandi, Dec 12 2011

a:= proc(n) option remember; local k;
       for k from 1+ `if`(n=1, -1, a(n-1))
       while not isprime(90*k+13) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2011

Select[Range[0,4000],PrimeQ[90 #+13]&] (* Vincenzo Librandi, Dec 12 2011 *)

is(n)=isprime(90*n+13) \\ Charles R Greathouse IV, Jul 12 2016

A201817 Numbers k such that 90*k + 67 is prime.

Original entry on oeis.org

0, 1, 3, 6, 8, 9, 10, 13, 14, 17, 19, 20, 23, 29, 30, 31, 33, 35, 36, 42, 44, 47, 50, 51, 56, 57, 61, 62, 63, 64, 66, 69, 70, 72, 73, 76, 77, 79, 83, 85, 90, 94, 96, 98, 100, 101, 103, 107, 108, 110, 117, 118, 120, 121, 122, 125, 127, 128, 129, 133, 138, 139

Offset: 1

J. W. Helkenberg, Dec 05 2011

Looking at the format 90*k + 67 modulo 9 and modulo 10 we see that all entries of A142323 have digital root 4 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816.

[n: n in [0..200] | IsPrime(90*n+67)]; // Vincenzo Librandi, Dec 12 2011

a:= proc(n) option remember; local k;
       for k from 1+ `if`(n=1, -1, a(n-1))
       while not isprime(90*k+67) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Dec 06 2011

Select[Range[0,4000],PrimeQ[90 #+67]&] (* Vincenzo Librandi, Dec 12 2011 *)

is(n)=isprime(90*n+67) \\ Charles R Greathouse IV, Feb 17 2017

A201820 Numbers k such that 90*k + 23 is prime.

Original entry on oeis.org

0, 1, 3, 4, 6, 7, 8, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 25, 28, 29, 32, 34, 39, 40, 42, 45, 47, 50, 52, 53, 55, 57, 59, 63, 64, 67, 68, 70, 76, 78, 84, 85, 87, 90, 95, 96, 97, 99, 102, 103, 105, 108, 109, 110, 112, 113, 116, 119, 122, 123, 125, 129, 131

Offset: 1

J. W. Helkenberg, Dec 05 2011

This sequence was generated by adding 12 Fibonacci-like sequences. Looking at the format 90*k+23 modulo 9 and modulo 10 we see that all entries of A142324 have digital root 5 and last digit 3. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818.

[n: n in [0..200] | IsPrime(90*n+23)]; // Vincenzo Librandi, Dec 11 2011

Select[Range[0,400],PrimeQ[90 #+23]&] (* Vincenzo Librandi, Dec 11 2011 *)

is(n)=isprime(90*n+23) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A142324(n) - 23)/90.

A201822 Numbers k such that 90*k + 77 is prime.

Original entry on oeis.org

1, 2, 3, 6, 8, 9, 10, 15, 17, 18, 19, 20, 24, 26, 29, 30, 32, 34, 37, 40, 41, 43, 45, 46, 48, 54, 58, 59, 60, 62, 65, 68, 69, 74, 75, 76, 79, 82, 83, 85, 86, 87, 89, 93, 94, 95, 97, 102, 104, 109, 111, 113, 114, 115, 117, 122, 128, 130, 131, 135, 138, 144

Offset: 1

J. W. Helkenberg, Dec 05 2011

Looking at the format 90k+77 modulo 9 and modulo 10 we see that all entries of A142329 have digital root 5 and last digit 7. (Reverting the process is an application of the Chinese remainder theorem.)

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A181732, A198382, A195993, A196000, A196007, A201739, A201734, A201804, A201816, A201817, A201818, A201820.

[n: n in [0..200] | IsPrime(90*n+77)]; // Vincenzo Librandi, Dec 11 2011

Select[Range[0,400],PrimeQ[90 #+77]&] (* Vincenzo Librandi, Dec 11 2011 *)

is(n)=isprime(90*n+77) \\ Charles R Greathouse IV, Feb 17 2017

a(n) = (A142329(n) - 77)/90.

cp's OEIS Frontend

A195993 Numbers n such that 90n + 73 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A196000 Numbers k such that 90*k + 19 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A196007 Numbers n such that 90n + 83 is prime.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A201734 Numbers n such that 90*n + 47 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A201739 Numbers n such that 90*n + 29 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Formula

A201804 Numbers k such that 90*k + 11 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Extensions

A201816 Numbers k such that 90*k + 13 is prime.

Views

Author

Keywords

Comments

Links

Crossrefs