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

Author

Enoch Haga, Sep 23 2007

Keywords

• easy
• nonn
• base

Comments

Breaks occur in the monotonic sequence at 2897, 12277, 12511, 24499, etc.

Each prime is exactly two digits longer than the embedded central prime.

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, ....
		

Crossrefs

Cf. A133782, A075595.

Programs

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