A383979 -id:A383979 - cp's OEIS frontend

A383978 Primes with at least two identical trailing digits.

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

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

A384016 a(n) is the number of n-digit terms in A384015.

Original entry on oeis.org

0, 1, 0, 0, 74, 673, 5851, 50977, 451608, 4048657, 36675547, 335269867, 3087739250, 28615970101, 266630103368, 2495975596632

Offset: 1

Stefano Spezia, May 17 2025

Cf. A383979, A384014, A384015.

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],l=IntegerLength[k]]==Part[d,l-1] &&Part[d,1]==Part[d,2],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(1, 10) for j in range(i*11*10**(n-2), (i*11+1)*10**(n-2), 100) for k in (11, 33, 77, 99) if isprime(j+k))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, May 19 2025

a(11) from David Radcliffe, May 18 2025
a(12)-a(13) from Michael S. Branicky, May 19 2025
a(14) from Michael S. Branicky, May 22 2025
a(15) from Lyle Blosser, Aug 24 2025
a(16) from Lyle Blosser, Aug 30 2025

cp's OEIS Frontend

A383978 Primes with at least two identical trailing digits.

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Extensions

A384016 a(n) is the number of n-digit terms in A384015.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python

Extensions