A383782 a(n) is the number of n-digit terms in A383781.

4, 10, 30, 147, 408, 1823, 4353, 17690, 38419, 143219, 284441, 980166, 1806038, 5813294, 10037352, 30426498, 49595776, 142437454, 220519428, 603013312, 890961094, 2329755538

Offset: 1

Author

Stefano Spezia, May 09 2025

Keywords

• nonn
• base
• more

Comments

After the first two terms, the ratios between successive odd terms and the ratios between successive even terms are decreasing. - Michael S. Branicky, May 11 2025

Crossrefs

Cf. A383781.

Programs

Mathematica

Unprotect[CompositeQ]; CompositeQ[1]:=True; Protect[CompositeQ]; Q[n_]:=And[AllTrue[FromDigits/@Table[Take[IntegerDigits[n], -i], {i,IntegerLength[n],1,-2}], PrimeQ], AllTrue[FromDigits/@Table[Take[IntegerDigits[n], -i], {i,IntegerLength[ n]-1,1,-2}], CompositeQ]]; a[n_]:=Module[{p=Prime[PrimePi[10^(n-1)]+1], k=0}, While[10^(n-1)<=p<10^n-1, If[Q[p], k++]; p=NextPrime[p]]; k]; Array[a,7]

Python

from gmpy2 import is_prime, mpz
from itertools import count, islice
def agen():
    olst, elst = [2, 3, 5, 7], [11, 19, 29, 31, 41, 59, 61, 71, 79, 89]
    yield from (len(olst), len(elst))
    for n in count(1):
        olst2, elst2 = [], []
        for o in olst:
            o, base = o, 10**(2*n-1)
            for i in range(10*base, 100*base, base):
                t = i + o
                t2 = int(str(t)[1:])
                if is_prime(t) and not is_prime(t2):
                    olst2.append(t)
        yield len(olst2)
        for e in elst:
            e, base = e, 10**(2*n)
            for i in range(10*base, 100*base, base):
                t = i + e
                t2 = int(str(t)[1:])
                if is_prime(t) and not is_prime(t2):
                    elst2.append(t)
        yield len(elst2)
        olst, elst = sorted(olst2), sorted(elst2)
print(list(islice(agen(), 12))) # Michael S. Branicky, May 11 2025

Extensions

a(11)-a(19) from Michael S. Branicky, May 11 2025

a(20)-a(22) from Michael S. Branicky, May 19 2025