A384016 -id:A384016 - cp's OEIS frontend

A383979 a(n) is the number of n-digit terms in A383978.

0, 1, 15, 106, 821, 6909, 58683, 509654, 4508611, 40421003, 366300162, 3348975103, 30845805300, 285887726304, 2663962455651, 24939375901980

Offset: 1

Stefano Spezia, May 16 2025

Lyle Blosser, Python script

Cf. A383978, A384014, A384016.

a[n_]:=Module[{count=0},For[k=Prime[PrimePi[10^(n-1)]+1], k<=Prime[PrimePi[10^n-1]],k=NextPrime[k],If[Part[d=IntegerDigits[k],l=IntegerLength[k]]==Part[d,l-1],count++]]; count]; Array[a,7]

from sympy import isprime
def a(n):
    if n < 3: return n-1
    return sum(1 for i in range(10**(n-1), 10**n, 100) for k in (11, 33, 77, 99) if isprime(i+k))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, May 20 2025

a(12) from Michael S. Branicky, May 20 2025
a(13) from Michael S. Branicky, May 27 2025
a(14)-a(15) from Lyle Blosser, Jul 09 2025
a(15) corrected by Lyle Blosser, Aug 09 2025
a(16) from Lyle Blosser, Aug 23 2025

A384014 a(n) is the number of n-digit terms in A384013.

Original entry on oeis.org

0, 1, 16, 108, 834, 6893, 58659, 510839, 4515301, 40477023, 366751460, 3352789726, 30877698604, 286159371452, 2666303391801, 24959756192476, 234610874384116, 2213224276178123, 20945897352118544, 198802912201260034, 1891788092230264832, 18044365524165259927, 172479703095316537972

Offset: 1

Stefano Spezia, May 17 2025

Tomás Oliveira e Silva, Tables of values of pi(x) and of pi2(x)

Cf. A383979, A384013, A384016.

a[1]:=0; a[n_]:=Module[{count=0},For[k=Prime[PrimePi[10^(n-1)]+1], k<=Prime[PrimePi[10^n-1]],k=NextPrime[k],If[Part[d=IntegerDigits[k],1]==Part[d,2],count++]]; count]; Array[a,7]

a(11)-a(23) from David Radcliffe, May 17 2025

A384015 Primes with at least two identical trailing digits and at least two identical leading digits.

Original entry on oeis.org

11, 11177, 11299, 11311, 11399, 11411, 11633, 11677, 11699, 11777, 11833, 11933, 22111, 22133, 22277, 22433, 22511, 22699, 22777, 22811, 22877, 33199, 33211, 33311, 33377, 33533, 33577, 33599, 33811, 33911, 44111, 44533, 44633, 44699, 44711, 44777, 55333, 55399

Offset: 1

Stefano Spezia, May 17 2025

Cf. A383978, A384013, A384016.

Subsequence of A050758.

Select[Prime[Range[5,6000]],Part[d=IntegerDigits[#],l=IntegerLength[#]]==Part[d,l-1] && Part[d,1]==Part[d,2] &]

from itertools import count, islice
from sympy import isprime
def A384015_gen(): # generator of terms
    yield 11
    for n in count(2):
        yield from filter(isprime,(i+j+k for i in range(11*10**(n-2),11*10**(n-1),11*10**(n-2)) for j in range(0,10**(n-2),100) for k in (11,33,77,99)))
A384015_list = list(islice(A384015_gen(),38)) # Chai Wah Wu, May 20 2025

cp's OEIS Frontend

A383979 a(n) is the number of n-digit terms in A383978.

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A384014 a(n) is the number of n-digit terms in A384013.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A384015 Primes with at least two identical trailing digits and at least two identical leading digits.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python