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A086043 Concatenation of first n twin primes. 3
3, 35, 357, 35711, 3571113, 357111317, 35711131719, 3571113171929, 357111317192931, 35711131719293141, 3571113171929314143, 357111317192931414359, 35711131719293141435961, 3571113171929314143596171, 357111317192931414359617173, 357111317192931414359617173101 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 6 21:32 EDT 2022. Contains 357270 sequences. (Running on oeis4.)