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A089777 a(n) = smallest prime of the form n followed by a prime. 2


%S 13,23,37,43,53,67,73,83,97,103,113,127,137,1423,157,163,173,1811,193,

%T 2011,2111,223,233,2411,257,263,277,283,293,307,313,3217,337,347,353,

%U 367,373,383,397,4013,4111,4211,433,443,457,463,4723,487,4919,503,5113

%N a(n) = smallest prime of the form n followed by a prime.

%C Open problem(?): show that a(n) always exists.

%H T. D. Noe, <a href="/A089777/b089777.txt">Table of n, a(n) for n=1..10000</a>

%p cat2 := proc(a,b) local dgs ; dgs := max(1,ilog10(b)+1) ; a*10^dgs+b ; end: A089777 := proc(k) local i,p,q ; for i from 1 do p := ithprime(i) ; q := cat2(k,p) ; if isprime(q) then RETURN(q) ; fi; od: end: for k from 1 to 80 do printf("%d,",A089777(k)) ; od: # _R. J. Mathar_, Jan 05 2009

%t Table[k=2; While[p=FromDigits[Join[IntegerDigits[n],IntegerDigits[Prime[k]]]]; !PrimeQ[p], k++ ]; p, {n,100}] (* _T. D. Noe_, Jan 06 2009 *)

%Y Cf. A096915 (gives the primes that are appended to n). - _R. J. Mathar_, Jan 05 2009

%K base,easy,nonn

%O 1,1

%A _Amarnath Murthy_, Nov 24 2003

%E Extended by _T. D. Noe_ and _R. J. Mathar_, Jan 06 2009

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)