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 A073641 a(1) = 2; a(n) = smallest prime not included earlier such that concatenation of two successive terms is a prime. 3
 2, 3, 7, 19, 13, 61, 31, 37, 67, 79, 103, 43, 73, 127, 139, 97, 151, 157, 109, 199, 181, 193, 163, 211, 229, 223, 241, 271, 277, 331, 283, 397, 337, 313, 307, 367, 457, 421, 349, 373, 379, 433, 439, 409, 463, 523, 487, 601, 541, 547, 499, 571, 673, 613, 577 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Conjecture: every prime besides 5 is in this list. - Gabriel Cunningham (gcasey(AT)mit.edu), Apr 11 2003 It appears that the terms belong to A007645. There are no primes of form 6k-1 in this sequence. - Alexander Adamchuk, Aug 15 2006 The above conjecture by Cunningham (Apr 11 2003) is false: Since a(2)=3 and a(3)=7 == 1 mod 6, all subsequent terms must also be 1 mod 6 because concatenations of numbers 1 mod 6 with 5 mod 6 are 0 mod 3. - Bob Selcoe, Aug 25 2015 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A075609(n) for n>1. - Alexander Adamchuk, Aug 15 2006 MAPLE N:= 10000: # to get all terms before the first one > N A:= 2: Primes:= Vector(select(isprime, [seq(2*i+1 , i=1..floor((N-1)/2))])): Nprimes:= LinearAlgebra:-Dimension(Primes): Next:= Vector(Nprimes): Prev:= Vector(Nprimes): for i from 1 to Nprimes-1 do Next[i]:= i+1; Prev[i+1]:= i od: first:= 1: found:= true: for n from 2 while found do   i:= first;   found:= false;   while i <> 0 do     p:= Primes[i];     if isprime(10^(1+ilog10(p))*A[n-1] + p) then       found:= true;       A[n]:= p;       if i = first then first:= Next[first]       else Next[Prev[i]]:= Next[i]       fi;       if Next[i] <> 0 then         Prev[Next[i]]:= Prev[i]       fi;       break     fi;     i:= Next[i];   od od: seq(A[i], i=1..n-2); # Robert Israel, Aug 25 2015 MATHEMATICA t = {2}; Do[i = 2; While[! PrimeQ[FromDigits[Flatten[IntegerDigits[{Last[t], x = Prime[i]}]]]] || MemberQ[t, x], i++]; AppendTo[t, x], {54}]; t (* Jayanta Basu, Jul 03 2013 *) CROSSREFS Cf. A000040, A075609. Sequence in context: A096203 A328430 A143874 * A273006 A117763 A165571 Adjacent sequences:  A073638 A073639 A073640 * A073642 A073643 A073644 KEYWORD base,nonn AUTHOR Amarnath Murthy, Aug 09 2002 EXTENSIONS More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 11 2003 Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003 STATUS approved

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Last modified February 21 01:03 EST 2020. Contains 332086 sequences. (Running on oeis4.)