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%I #6 Mar 31 2012 10:22:32
%S 23,37,53,73,127,139,149,151,157,163,167,173,181,191,193,197,199,211,
%T 223,227,229,233,241,251,257,263,269,271,277,283,307,313,331,337,347,
%U 349,353,373,379,383,389,401,421,431,433,439,443,449,457,461,463,467,487,491,499
%N (k+1)-digit primes which can be represented by 10*q+r where q and r are k-digit primes.
%C There may be more than one representation of that kind,
%C for example 2791 = 10*233+461 = 10*239+401 = 10*268+101 = 10*227+521 = 10*251+281 splits the 4-digit prime 2791 into two 3-digit primes in 5 different ways; only one instance (only one 2791 in the example) is added to the sequence then.
%e a(1)=23 = 10*2+3. a(3)= 53 = 10*5+3. a(5)= 127 = 11*10+17. 167= 10*13+37.
%p A055642 := proc(n) max(1,ilog10(n)+1) ; end:
%p isA129351 := proc(p) local np1,q,r ; if isprime(p) then np1 := A055642(p)-1 ; q := nextprime(10^(np1-1)) ; while q < 10^np1 do r := q ; while r < 10^np1 do if 10*q+r = p or 10*r+q = p then return true; end if ; r := nextprime(r) ; end do ; q := nextprime(q) ; end do ; false ; else false; end if; end proc:
%p for n from 5 to 400 do p := ithprime(n) ; if isA129351(p) then printf("%d,",p) ; fi; od: # _R. J. Mathar_, Nov 02 2009
%K nonn,easy,base
%O 1,1
%A _J. M. Bergot_, May 28 2007
%E Edited, 139 inserted and sequence extended - _R. J. Mathar_, Nov 02 2009
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