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A383780 a(n) is the number of n-digit terms in A383779.

%I A383780 #45 May 16 2025 15:54:29
%S A383780 4,12,46,103,396,717,2451,3929,11803,17202,46916,62668,157138,197114,
%T A383780 458064,541267,1180018,1323543,2718398,2915696,5675113,5839596,
%U A383780 10821575,10724938,18983655,18174231,30856021,28608908,46708476,42036009,66157433,57908390,88020231,75070514
%N A383780 a(n) is the number of n-digit terms in A383779.
%C A383780 Conjecture: A383779 is finite, since after the first two terms here, the ratios between successive odd terms and the ratios between successive even terms are quickly decreasing. - _Michael S. Branicky_, May 11 2025
%C A383780 Indeed, a(n) < a(n-2) for n = 45..55 (see b-file). - _Michael S. Branicky_, May 15 2025
%C A383780 A383779 is finite with 3356513448 terms (summing terms of b-file); a(n) = 0 for n >= 114. - _Michael S. Branicky_, May 16 2025
%H A383780 Michael S. Branicky, <a href="/A383780/b383780.txt">Table of n, a(n) for n = 1..115</a>
%t A383780 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]
%o A383780 (Python)
%o A383780 from gmpy2 import is_prime, mpz
%o A383780 from itertools import count, islice
%o A383780 def agen():
%o A383780     olst, elst = [2, 3, 5, 7], [11, 13, 17, 19, 41, 43, 47, 61, 67, 83, 89, 97]
%o A383780     yield from (len(olst), len(elst))
%o A383780     for n in count(1):
%o A383780         olst2, elst2 = [], []
%o A383780         for o in olst:
%o A383780             for i in range(1, 100, 2):
%o A383780                 t = 100*o + i
%o A383780                 if is_prime(t) and not is_prime(t//10):
%o A383780                     olst2.append(t)
%o A383780         yield len(olst2)
%o A383780         for e in elst:
%o A383780             for i in range(100):
%o A383780                 t = 100*e + i
%o A383780                 if is_prime(t) and not is_prime(t//10):
%o A383780                     elst2.append(t)
%o A383780         yield len(elst2)
%o A383780         olst, elst = olst2, elst2
%o A383780 print(list(islice(agen(), 16))) # _Michael S. Branicky_, May 11 2025
%Y A383780 Cf. A383779.
%K A383780 nonn,base
%O A383780 1,1
%A A383780 _Stefano Spezia_, May 09 2025
%E A383780 a(12) and beyond from _Michael S. Branicky_, May 11 2025