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Search: id:A133781
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| A133781 |
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Prime sequence overlaying the central digits of prime numbers in monotonically increasing order (when breaks occur the monotonic sequence begins again and continues). |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Breaks occur in the montotonic sequence at 2897, 12277, 12511, 24499, etc. Each prime is exactly two digits longer than the embedded central prime.
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FORMULA
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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.
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EXAMPLE
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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, ....
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PROGRAM
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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
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CROSSREFS
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Cf. A133782.
Adjacent sequences: A133778 A133779 A133780 this_sequence A133782 A133783 A133784
Sequence in context: A077360 A102636 A075595 this_sequence A126096 A006285 A094933
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KEYWORD
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easy,nonn,uned
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AUTHOR
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Enoch Haga (Enokh(AT)comcast.net), Sep 23 2007
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