A384013 -id:A384013 - cp's OEIS frontend

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

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

A383978 Primes with at least two identical trailing digits.

Original entry on oeis.org

11, 199, 211, 233, 277, 311, 433, 499, 577, 599, 677, 733, 811, 877, 911, 977, 1033, 1277, 1399, 1433, 1499, 1511, 1699, 1733, 1777, 1811, 1877, 1933, 1999, 2011, 2099, 2111, 2311, 2333, 2377, 2399, 2411, 2477, 2633, 2677, 2699, 2711, 2777, 2833, 2999, 3011, 3299

Offset: 1

Stefano Spezia, May 16 2025

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

Cf. A131306, A383979, A384013, A384015.
Subsequence of A050758.
Cf. A061022 (variant).

select(isprime, [seq(seq(i*100 + j*11, j = [1,3,7,9]),i=0..100)]); # Robert Israel, May 17 2025

Select[Prime[Range[500]],Part[d=IntegerDigits[#],l=IntegerLength[#]]==Part[d,l-1] &]

from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
    yield from filter(isprime, (i+k for i in count(0, 100) for k in (11, 33, 77, 99)))
print(list(islice(agen(), 50))) # Michael S. Branicky, May 20 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

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

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A383978 Primes with at least two identical trailing digits.

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

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Mathematica

Python