A055781 -id:A055781 - cp's OEIS frontend

A038800 Number of primes between 10n and 10n+9.

4, 4, 2, 2, 3, 2, 2, 3, 2, 1, 4, 1, 1, 3, 1, 2, 2, 2, 1, 4, 0, 1, 3, 2, 1, 2, 2, 2, 2, 1, 1, 3, 0, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 3, 2, 1, 3, 1, 1, 2, 2, 0, 2, 0, 2, 1, 2, 2, 1, 2, 2, 3, 0, 1, 3, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 4, 1, 0, 3, 1, 1, 3, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 1

Offset: 0

Jeff Burch

If n runs through the primes, the subsequence 2, 2, 2, 3, 1, 3, 2, 4, 2, 1, 3, 2, 1, 3, 1, 0, 2, 3, 2,... is created. - R. J. Mathar, Jul 19 2012

Since 431, 433, and 439 are all prime, a(43)=3. - Bobby Jacobs, Sep 25 2016

Michael De Vlieger, Table of n, a(n) for n = 0..10000
A. Frank and P. Jacqueroux, International Contest, 2001. Numerators of Item 23

Cf. A055781, A055782, A055783, A055784.
Positions of 4's: {0} U A007811.
Cf. A098592.

Table[Count[Range[10 n, 10 n + 9], p_ /; PrimeQ@ p], {n, 0, 105}] (* Michael De Vlieger, Sep 25 2016 *)
Table[PrimePi[10n+9]-PrimePi[10n],{n,0,120}] (* Harvey P. Dale, May 04 2025 *)

a(n) = primepi(10*n+9) - primepi(10*n); \\ Michel Marcus, Sep 26 2016

a(43) corrected by Bobby Jacobs, Sep 25 2016

a(101) and a(104) corrected by Michael De Vlieger, Sep 25 2016

A023237 Primes p such that 10*p + 1 is also prime.

Original entry on oeis.org

3, 7, 13, 19, 31, 43, 97, 103, 109, 151, 157, 181, 193, 211, 241, 271, 337, 349, 367, 409, 421, 439, 487, 523, 547, 571, 601, 613, 631, 691, 733, 769, 811, 823, 829, 883, 937, 1009, 1021, 1033, 1039, 1063, 1069, 1117, 1201, 1249, 1279, 1291, 1459, 1483, 1489

Offset: 1

David W. Wilson

Primes which with a 1 appended stay prime.
Corresponding values of 10n + 1 in A055781. - Jaroslav Krizek, Jul 14 2010
Subsequence of A024912. - Michel Marcus, May 21 2014

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A024912, A055781, A105435, A005384 (2*p + 1), A158017 (10*p - 1).

[n: n in [0..1000] | IsPrime(n) and IsPrime(10*n+1)]; // Vincenzo Librandi, Nov 20 2010

[p: p in PrimesUpTo(1100)| IsPrime(10*p+1)]; // Vincenzo Librandi, May 21 2014

with(numtheory); for i from 1 to 500 do if isprime(10*ithprime(i)+1) then printf(`%d,`, ithprime(i)) fi: od: # James Sellers, Apr 09 2005

Select[Prime[Range[ 240]], PrimeQ[FromDigits[Join[IntegerDigits[ # ], {1}]]] &] (* Robert G. Wilson v, Apr 09 2005 *)
Select[Prime[Range[900]], PrimeQ[10 # + 1] &] (* Vincenzo Librandi, May 21 2014 *)

Edited by N. J. A. Sloane at the suggestion of M. F. Hasler, Aug 24 2007

A175355 Noncomposite reverse concatenations of divisors of n, sorted by n.

Original entry on oeis.org

1, 31, 421, 71, 131, 191, 2551, 311, 391331, 431, 48241612864321, 911371, 971, 1031, 1091, 1173913931, 1511, 1571, 1811, 1931, 2111, 2411, 24412261421, 24719131, 2711, 289171, 29214673421, 3014371, 30910331, 32565251351, 3371, 3491, 3671

Offset: 1

Jaroslav Krizek, Apr 20 2010

			For n = 9; a(9) = 391331 because A089374(9) = 39 and divisors of 39 are 1, 3, 13, 39; reverse concatenation of divisors A176558(21) = 391331 is noncomposite.

Robert Israel, Table of n, a(n) for n = 1..10000

Subsequence of A176558(n). Supersequence of A055781.

rcd:= proc(n) local D,T,i;
  D:= sort(convert(numtheory:-divisors(n),list));
  T:= D[1];
  for i from 2 to nops(D) do
    T:= T + 10^(1+ilog10(T))*D[i]
  od;
  T
end proc:
select(t -> t=1 or isprime(t), map(rcd, [$1..1000])); # Robert Israel, Aug 12 2020

a(n) = A176558(A089374(n)).

a(n) = A069582(n-1), n>1. [R. J. Mathar, May 03 2010]

Edited by Charles R Greathouse IV, Apr 30 2010

A214342 Count of the decimal descendants of the n-th prime.

Original entry on oeis.org

23, 22, 11, 23, 1, 14, 4, 40, 15, 6, 7, 13, 1, 14, 5, 0, 9, 16, 11, 4, 15, 1, 1, 0, 3, 10, 28, 0, 12, 0, 8, 1, 1, 9, 5, 1, 4, 1, 0, 2, 0, 6, 2, 5, 10, 19, 3, 5, 5, 6, 8, 5, 7, 0, 5, 3, 5, 8, 4, 1, 2, 5, 1, 2, 2, 0, 9, 5, 0, 7, 7, 2, 11, 9, 2, 2, 0, 0, 4, 28, 0, 7

Offset: 1

Alex Ratushnyak, Jul 12 2012

Prime q is a decimal descendant of prime p if q = p*10+k and 0<=k<=9.
The number of direct decimal descendants is A038800(p).
a(n) is the total count of direct decimal descendants of the n-th prime that are also prime, plus their decimal descendants that are prime, and so on.
Conjecture: no terms bigger than 35 after a(8)=40.

			prime(3)=5 has eleven descendants: 53, 59, 593, 599, 5939, 59393, 59399, 593933, 593993, 5939333, 59393339. So a(3)=11. All candidates of the form 5nnn1 and 5nnn7 are divisible by 3.
prime(5)=11, the only decimal descendant of 11 that is prime is 113, and because there are no primes between 1130 and 1140, a(5)=1.

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

Cf. A214280, A055781, A055782, A055783, A055784.

A214342 := proc(n)
    option remember;
    local a,p,k,d ;
    a := 0 ;
    p := ithprime(n) ;
    for k from 0 to 9 do
        d := 10*p+k ;
        if isprime(d) then
            a := a+1+procname(numtheory[pi](d)) ;
        end if;
    end do:
    return a;
end proc: # R. J. Mathar, Jul 19 2012

Table[t = {Prime[n]}; cnt = 0; While[t = Select[Flatten[Table[10*i + {1, 3, 7, 9}, {i, t}]], PrimeQ]; t != {}, cnt = cnt + Length[t]]; cnt, {n, 100}] (* T. D. Noe, Jul 24 2012 *)

A158014 Primes p such that (p-1)/8 is also prime.

Original entry on oeis.org

17, 41, 89, 137, 233, 569, 809, 857, 1049, 1097, 1193, 1433, 1913, 2153, 2777, 3209, 3449, 3593, 3833, 3929, 4073, 4457, 4793, 4937, 5273, 5417, 6089, 6473, 6569, 6857, 7433, 7529, 7577, 7817, 9209, 9497, 9833

Offset: 1

Roger L. Bagula, Mar 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A005385 for (p-1)/2, A090866 for (p-1)/4, A051644 for (p-1)/6, A055781 for (p-1)/10.

Flatten[Table[If[PrimeQ[n] && PrimeQ[(n - 1)/8], n, {}], {n, 1, 10000}]]
Select[Prime[Range[1500]], PrimeQ[(# - 1) / 8]&] (* Vincenzo Librandi, Apr 14 2013 *)

list(lim)=my(v=List()); forprime(p=2,(lim-1)\8, if(isprime(8*p+1), listput(v,8*p+1))); Vec(v) \\ Charles R Greathouse IV, Oct 20 2021

a(n)=8*A023228(n)+1. - R. J. Mathar, Mar 15 2009

a(n) >> n log^2 n. - Charles R Greathouse IV, Oct 21 2021

Edited by the Associate Editors of the OEIS, Apr 22 2009

A158018 Primes p such that (p - 1)/12 is also prime.

Original entry on oeis.org

37, 61, 157, 229, 277, 349, 373, 709, 733, 853, 877, 997, 1069, 1213, 1237, 1669, 1789, 2293, 2389, 2677, 2749, 2797, 3229, 3253, 3373, 3517, 3733, 4549, 4597, 4813, 4909, 5197, 5557, 5749, 6037, 6277, 6829, 7213, 7573, 7717, 7933, 8293, 8629, 9013, 9133

Offset: 1

Roger L. Bagula, Mar 11 2009

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A005385, A090866, A051644, A055781

Flatten[Table[If[PrimeQ[n] && PrimeQ[(n - 1)/12], n, {}], {n, 1, 10000}]]
Select[Prime[Range[1500]], PrimeQ[(# - 1) / 12]&] (* Vincenzo Librandi, Apr 14 2013 *)

a(n)=12*A075704(n)+1. [From R. J. Mathar, Mar 15 2009]

Definition slightly rephrased - The Assoc. Eds. of the OEIS, Aug 30 2010

cp's OEIS Frontend

A038800 Number of primes between 10n and 10n+9.

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A023237 Primes p such that 10*p + 1 is also prime.

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A175355 Noncomposite reverse concatenations of divisors of n, sorted by n.

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Maple

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A214342 Count of the decimal descendants of the n-th prime.

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Maple

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A158014 Primes p such that (p-1)/8 is also prime.

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PARI

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A158018 Primes p such that (p - 1)/12 is also prime.

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Mathematica

Formula

Extensions