cp's OEIS Frontend

A133781 Prime sequence overlaying the central digits of prime numbers. If possible, the value is greater than the previous one. Zero if no such embedding is possible.

%I A133781 #10 May 11 2023 10:27:02
%S A133781 127,131,151,173,1117,2131,2179,3191,4231,4297,6311,6373,7411,7433,
%T A133781 7477,7537,7591,9613,9677,9719,9733,9791,9833,2897,2971,21011,21031,
%U A133781 31079,31091,31139,31271,31319,31379,31391,41491,41513,41579,51631,51673
%N A133781 Prime sequence overlaying the central digits of prime numbers. If possible, the value is greater than the previous one. Zero if no such embedding is possible.
%C A133781 Breaks occur in the monotonic sequence at 2897, 12277, 12511, 24499, etc.
%C A133781 Each prime is exactly two digits longer than the embedded central prime.
%F A133781 Overlay the prime sequence in the exact center of a larger monotonically increasing prime sequence. If a break occurs resume at the break point and continue.
%e A133781 a(5) is 1117 because the 5th prime, 11, overlays the central digits of 1117, exactly. The prime 1117 is in monotonically increasing order beginning 127, 131, 151, 173, 1117, ....
%o A133781 (UBASIC) 10 C=26:Q=str(C):T=443
%o A133781 20 'monotonically increasing primes
%o A133781 30 'centered in primes
%o A133781 40 'change val(m) in 100
%o A133781 50 'adjust T in line 10 after every break
%o A133781 60 N=101
%o A133781 70 A=3:S=sqrt(N)
%o A133781 80 B=N\A
%o A133781 90 if B*A=N then N=N+2:goto 70
%o A133781 100 A=A+2
%o A133781 110 if A<=sqrt(N) then 80
%o A133781 120 Z=str(N):W=alen(N):W=W-2:M=mid(Z,3,W): if M=Q then print C,N:stop
%o A133781 130 if val(M)=nxtprm(T) then print Q,M,Z:T=val(M):stop
%o A133781 140 C=C+1:Q=str(C)
%o A133781 150 N=N+2:goto 70
%Y A133781 Cf. A133782, A075595.
%K A133781 easy,nonn,base
%O A133781 1,1
%A A133781 _Enoch Haga_, Sep 23 2007
%E A133781 Edited by _Franklin T. Adams-Watters_, Oct 04 2012