cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A086043 Concatenation of first n twin primes.

Original entry on oeis.org

3, 35, 357, 35711, 3571113, 357111317, 35711131719, 3571113171929, 357111317192931, 35711131719293141, 3571113171929314143, 357111317192931414359, 35711131719293141435961, 3571113171929314143596171, 357111317192931414359617173, 357111317192931414359617173101
Offset: 1

Views

Author

Cino Hilliard, Sep 08 2003

Keywords

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

Crossrefs

Cf. A001097 (twin primes), A086080, A086158.
Cf. A007908, A019518, A059996, A078795, A089933, A092447.

Programs

  • 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 *)
  • 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",") ) ) }

Extensions

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

A089948 Smallest prime factor of the concatenation of the first n odd primes.

Original entry on oeis.org

3, 5, 3, 13, 3, 23, 3, 11, 7, 13, 3, 137, 3, 19, 41, 3, 29, 1087, 7, 23, 3, 641, 7, 79, 124516914725653, 1254907, 983, 691, 19, 9656610616812422838401, 11, 3, 19, 3, 4951, 83404036302541, 3, 372707, 53, 3, 17, 3, 6073, 3, 11, 37, 3
Offset: 1

Views

Author

Cino Hilliard, Jan 11 2004

Keywords

Comments

3 is the only number < 10000 whose concatenation of odd primes is prime. Conjecture: Beyond 3 the concatenation of odd primes produce only composite numbers.

Crossrefs

Cf. A089933.

Programs

  • Mathematica
    Join[{x=3},Table[First[First/@FactorInteger[x=FromDigits[Flatten[IntegerDigits[{x,Prime[n]}]]]]],{n,3,30}]] (* Jayanta Basu, Jun 04 2013 *)
  • PARI
    factorconcat(n) = { y=""; forprime(x=3,n, y=concat(Str(y),Str(x)); z=eval(y); a = component(factor(z),1); print1(a[1]",") ) }

Extensions

Edited and extended by Charles R Greathouse IV, Apr 29 2010

A132937 Concatenation of first n odd isolated primes.

Original entry on oeis.org

23, 2337, 233747, 23374753, 2337475367, 233747536779, 23374753677983, 2337475367798389, 233747536779838997, 233747536779838997113, 233747536779838997113127, 233747536779838997113127131
Offset: 1

Views

Author

Omar E. Pol, Sep 05 2007

Keywords

Links

Crossrefs

Isolated primes: A007510. Cf: A007908, A019518, A059996, A078795, A089933.

Programs

  • Mathematica
    With[{ips=Transpose[Select[Partition[Prime[Range[2,50]],3,1], Min[ Differences[#]]>2&]][[2]]},Table[FromDigits[Flatten[ IntegerDigits/@ Take[ips,n]]],{n,Length[ips]}]] (* Harvey P. Dale, Sep 17 2013 *)

A283801 Concatenation of the first n odd composite numbers (A071904).

Original entry on oeis.org

9, 915, 91521, 9152125, 915212527, 91521252733, 9152125273335, 915212527333539, 91521252733353945, 9152125273335394549, 915212527333539454951, 91521252733353945495155, 9152125273335394549515557, 915212527333539454951555763, 91521252733353945495155576365
Offset: 1

Views

Author

XU Pingya, Mar 17 2017

Keywords

Comments

There are 3 primes in the first 5028 terms of this sequence, see A283802.

Links

Crossrefs

Cf. A071904, A089933, A132932.

Programs

  • Mathematica
    bb[1]=9;bb[n_]:=bb[n]=Which[PrimeQ[bb[n-1]+2]==False,bb[n-1]+2,PrimeQ[bb[n-1]+4]==False,bb[n-1]+4,True,bb[n-1]+6];coc[n_]:=FromDigits[Flatten[IntegerDigits[Table[bb[k],{k,1,n}]]]];Table[coc[n],14]
f[n_] := Block[{oc = cc = 0, k = 2}, While[oc <= n, If[ OddQ@ k && !PrimeQ@ k, cc = cc*10^IntegerLength[k] +k; oc++]; k++]; cc]; Array[f, 14] (* Robert G. Wilson v, Mar 17 2017 *)

A132931 Concatenation of first n Mersenne primes.

Original entry on oeis.org

3, 37, 3731, 3731127, 37311278191, 37311278191131071, 37311278191131071524287, 373112781911310715242872147483647, 3731127819113107152428721474836472305843009213693951
Offset: 1

Views

Author

Omar E. Pol, Sep 05 2007

Keywords

Links

Crossrefs

Mersenne primes: A000668. Cf. A007908, A019518, A059996, A078795, A089933.

Programs

  • Mathematica
    Module[{nn=15,mp},mp=2^MersennePrimeExponent[Range[nn]]-1;Table[FromDigits[Flatten[ IntegerDigits/@Take[mp,n]]],{n,nn}]] (* Harvey P. Dale, Aug 25 2023 *)

A132933 Concatenation of first n primes whose digits are primes.

Original entry on oeis.org

2, 23, 235, 2357, 235723, 23572337, 2357233753, 235723375373, 235723375373223, 235723375373223227, 235723375373223227233, 235723375373223227233257, 235723375373223227233257277, 235723375373223227233257277337
Offset: 1

Views

Author

Omar E. Pol, Sep 05 2007

Keywords

Crossrefs

Primes whose digits are primes: A019546. Cf. A007908, A019518, A019546, A089933.

A132936 Concatenation of first n isolated primes.

Original entry on oeis.org

2, 223, 22337, 2233747, 223374753, 22337475367, 2233747536779, 223374753677983, 22337475367798389, 2233747536779838997, 2233747536779838997113, 2233747536779838997113127
Offset: 1

Views

Author

Omar E. Pol, Sep 05 2007

Keywords

Links

Crossrefs

Isolated primes: A007510. Cf: A007908, A019518, A059996, A078795, A089933.
Showing 1-7 of 7 results.

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