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.
127, 131, 151, 173, 1117, 2131, 2179, 3191, 4231, 4297, 6311, 6373, 7411, 7433, 7477, 7537, 7591, 9613, 9677, 9719, 9733, 9791, 9833, 2897, 2971, 21011, 21031, 31079, 31091, 31139, 31271, 31319, 31379, 31391, 41491, 41513, 41579, 51631, 51673
Offset: 1
Examples
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, ....
Programs
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UBASIC
10 C=26:Q=str(C):T=443 20 'monotonically increasing primes 30 'centered in primes 40 'change val(m) in 100 50 'adjust T in line 10 after every break 60 N=101 70 A=3:S=sqrt(N) 80 B=N\A 90 if B*A=N then N=N+2:goto 70 100 A=A+2 110 if A<=sqrt(N) then 80 120 Z=str(N):W=alen(N):W=W-2:M=mid(Z,3,W): if M=Q then print C,N:stop 130 if val(M)=nxtprm(T) then print Q,M,Z:T=val(M):stop 140 C=C+1:Q=str(C) 150 N=N+2:goto 70
Formula
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.
Extensions
Edited by Franklin T. Adams-Watters, Oct 04 2012
Comments