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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[1]:= 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: A186232 A160181 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 March 26 10:57 EDT 2019. Contains 321491 sequences. (Running on oeis4.)