A086043 Concatenation of first n twin primes.

3, 35, 357, 35711, 3571113, 357111317, 35711131719, 3571113171929, 357111317192931, 35711131719293141, 3571113171929314143, 357111317192931414359, 35711131719293141435961, 3571113171929314143596171, 357111317192931414359617173, 357111317192931414359617173101

Offset

1,1

Comments

After 3, 357111317192931414359 is the only prime in the sequence for n up to 10000.

Although 5 appears in two twin prime pairs (3, 5) and (5, 7), 5 is concatenated only once in the sequence. - Daniel Forgues, Aug 23 2016

a(n) == 0 mod 3 for n odd, a(n) == 2 mod 3 for n even. - Robert Israel, Sep 01 2016

Links

Robert Israel, Table of n, a(n) for n = 1..270

C. K. Caldwell, Twin Primes.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Maple

Primes:= select(isprime, {seq(i, i=1..100, 2)}):
T1:= Primes intersect map(`+`, Primes, 2):
Twins:= sort(convert(T1 union map(`-`, T1, 2), list)):
dcat:= (a, b) -> a*10^(1+ilog10(b))+b:
A[1]:= 3:
for n from 2 to nops(Twins) do A[n]:= dcat(A[n-1], Twins[n]) od:
seq(A[i], i=1..nops(Twins)); # Robert Israel, Sep 01 2016

Mathematica

Table[FromDigits@ Flatten@ Map[IntegerDigits, Take[#, n]], {n, Length@ #}] &[Union@ Join[#, # + 2] &@ Select[Prime@ Range@ 17, NextPrime@ # - 2 == # &]] (* Michael De Vlieger, Sep 01 2016 *)
Module[{tps=Union[Flatten[Select[Partition[Prime[Range[50]], 2, 1], #[[2]]-#[[1]] == 2&]]]}, FromDigits[Flatten[IntegerDigits/@#]]&/@Table[Take[tps, n], {n, Length[tps]}]] (* Harvey P. Dale, Jun 16 2022 *)

Prog

(PARI) concattwprb(n) = { y=3; forprime(x=5, n, if(isprime(x+2) || isprime(x-2), y=eval(concat(Str(y), Str(x))); print1(y", ") ) ) }

Crossrefs

Cf. A001097 (twin primes), A086080, A086158.

Cf. A007908, A019518, A059996, A078795, A089933, A092447.

Sequence in context: A221922 A260586 A089933 * A221774 A221687 A221223

Adjacent sequences: A086040 A086041 A086042 * A086044 A086045 A086046

Keyword

easy,nonn,base

Author

Cino Hilliard, Sep 08 2003

Extensions

Edited by N. J. A. Sloane, Jul 01 2008 at the suggestion of R. J. Mathar

Status

approved