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

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

Offset: 1

Author

Stefano Spezia, May 17 2025

Keywords

• nonn
• base
• more
• changed

Crossrefs

Cf. A383979, A384014, A384015.

Programs

Mathematica

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]

Python

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

Extensions

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