A055784 -id:A055784 - 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

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 *)

cp's OEIS Frontend

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

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