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a(n) = p.q in decimal notation where p = prime(n) and q is the smallest prime (A066065(n)) such that the concatenation p.q is a prime.
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%I #21 Dec 08 2024 22:09:59

%S 23,37,53,73,113,137,173,193,233,293,313,373,4111,433,4723,5323,593,

%T 613,673,7129,733,797,8311,8923,977,1013,1033,10711,1093,11311,1277,

%U 13147,1373,13913,1493,15131,15731,1637,16729,1733,17911,18119,1913

%N a(n) = p.q in decimal notation where p = prime(n) and q is the smallest prime (A066065(n)) such that the concatenation p.q is a prime.

%H Harry J. Smith, <a href="/A066064/b066064.txt">Table of n, a(n) for n = 1..1000</a>

%e A000040(2) = 3 and as 32, 33 and 35 are composite, the next prime 7 = A066065(2) yields a(2) = 37.

%t Table[Block[{q = 3, d = IntegerDigits[p], k}, While[! PrimeQ@ Set[k, FromDigits[Join[d, IntegerDigits[q]]]], q = NextPrime@ q]; k], {p, Prime@ Range@ 43}] (* _Michael De Vlieger_, Jun 19 2018 *)

%o (PARI) a(n) = { my(p=prime(n)); forprime(q=3, oo, my(c=p*10^(logint(q,10)+1) + q); if(isprime(c), return(c))) } \\ _Harry J. Smith_, Nov 09 2009

%Y Cf. A066065.

%K base,nonn

%O 1,1

%A _Reinhard Zumkeller_, Dec 01 2001