A045532 -id:A045532 - cp's OEIS frontend

A075110 Concatenation of n-th prime and n in decimal notation.

21, 32, 53, 74, 115, 136, 177, 198, 239, 2910, 3111, 3712, 4113, 4314, 4715, 5316, 5917, 6118, 6719, 7120, 7321, 7922, 8323, 8924, 9725, 10126, 10327, 10728, 10929, 11330, 12731, 13132, 13733, 13934, 14935, 15136, 15737, 16338, 16739, 17340

Offset: 1

Reinhard Zumkeller, Sep 03 2002

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A045532.

a075110 n = read $ show (a000040 n) ++ show n :: Integer
-- Reinhard Zumkeller, Jul 08 2014

[Seqint(Intseq(n) cat Intseq(NthPrime(n))): n in [1..46]]; // Vincenzo Librandi, Mar 24 2019

Table[FromDigits[Join[IntegerDigits[Prime[n]], IntegerDigits[n]]], {n, 40}] (* Vincenzo Librandi, Mar 24 2019 *)

a(n) = eval(Str(prime(n), n)); \\ Michel Marcus, Mar 24 2019

a(n) = A000040(n)*10^(A004216(n)+1) + n.

A138821 Concatenation of n-th Fibonacci number and n-th prime.

Original entry on oeis.org

12, 13, 25, 37, 511, 813, 1317, 2119, 3423, 5529, 8931, 14437, 23341, 37743, 61047, 98753, 159759, 258461, 418167, 676571, 1094673, 1771179, 2865783, 4636889, 7502597, 121393101, 196418103, 317811107, 514229109, 832040113, 1346269127

Offset: 1

Omar E. Pol, Apr 05 2008, Apr 07 2008

			a(10)=5529 because A000045(10)=55 and A000040(10)=29.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A000045, A045532, A075110.

[Seqint(Intseq(NthPrime(n)) cat Intseq(Fibonacci(n))): n in [1..50]]; // Vincenzo Librandi, Jul 24 2019

f:= proc(n) local p;
  p:= ithprime(n);
  combinat:-fibonacci(n)*10^(1+ilog10(p))+p
end proc:
seq(f(n),n=1..100); # Robert Israel, Dec 15 2014

With[{nn=40},FromDigits[Flatten[IntegerDigits/@#]]&/@ Thread[ {Fibonacci[ Range[nn]],Prime[Range[nn]]}]] (* Harvey P. Dale, Dec 23 2011 *)

A138822 Concatenation of n-th prime and n-th Fibonacci number.

Original entry on oeis.org

21, 31, 52, 73, 115, 138, 1713, 1921, 2334, 2955, 3189, 37144, 41233, 43377, 47610, 53987, 591597, 612584, 674181, 716765, 7310946, 7917711, 8328657, 8946368, 9775025, 101121393, 103196418, 107317811, 109514229, 113832040, 1271346269

Offset: 1

Omar E. Pol, Apr 05 2008

			a(10)=2955 because A000040(10)=29 and A000045(10)=55.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040, A000045, A045532, A075110, A138821.

[Seqint(Intseq(Fibonacci(n)) cat Intseq(NthPrime(n))): n in [1..50]]; // Vincenzo Librandi, Jul 24 2019

With[{nn=50},FromDigits[Flatten[IntegerDigits[#]]]&/@Thread[ {Prime[ Range[ nn]],Fibonacci[Range[nn]]}]] (* Harvey P. Dale, Jul 12 2014 *)

A085451 Numbers n such that n and prime[n] together use only distinct digits.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 17, 19, 20, 21, 24, 25, 27, 28, 35, 39, 40, 45, 53, 57, 58, 60, 61, 69, 70, 72, 79, 85, 89, 90, 91, 93, 96, 98, 104, 108, 120, 124, 145, 146, 147, 150, 162, 236, 237, 253, 254, 259, 315, 316, 359, 380, 384, 390, 405, 406, 460, 461, 518

Offset: 1

Zak Seidov, Jul 01 2003

There are exactly 101 such numbers in the sequence. Numbers with distinct digits in A010784. Primes with distinct digits in A029743. The case n and n^2 (exactly 22 numbers) in A059930.

A178788(A045532(a(n))) = 1. [From Reinhard Zumkeller, Jun 30 2010]

			3106 is in the sequence (and the last term) because it and prime[3106]=28549 together use all 10 distinct digits.

Giovanni Resta, Table of n, a(n) for n = 1..101 (full sequence)

Cf. A010784 A029743 A059930 A085452.

bb = {}; Do[idpn = IntegerDigits[Prime[n]]; idn = IntegerDigits[n]; If[Length[idn] + Length[idpn] == Length[Union[idn, idpn]], bb = {bb, n}], {n, 1, 100000}]; Flatten[bb]

A139114 Concatenation of n-th Fibonacci number and n.

Original entry on oeis.org

11, 12, 23, 34, 55, 86, 137, 218, 349, 5510, 8911, 14412, 23313, 37714, 61015, 98716, 159717, 258418, 418119, 676520, 1094621, 1771122, 2865723, 4636824, 7502525, 12139326, 19641827, 31781128, 51422929, 83204030, 134626931, 217830932

Offset: 1

Omar E. Pol, Apr 09 2008

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000027, A000045, A045532, A075110, A138821, A138822, A139113.

#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@Table[{Fibonacci[n],n},{n,40}] (* Harvey P. Dale, Nov 03 2016 *)

A154963 Primes p such that the concatenation of p and prime(p) is prime.

Original entry on oeis.org

2, 17, 23, 41, 61, 71, 83, 127, 227, 337, 353, 499, 503, 571, 727, 887, 911, 937, 971, 1061, 1427, 1579, 1663, 1693, 1709, 1871, 1877, 1907, 1949, 1973, 2017, 2063, 2081, 2239, 2339, 2393, 2467, 2713, 2797, 2939, 2999, 3181, 3271, 3463, 3643, 3659, 3677

Offset: 1

Juri-Stepan Gerasimov, Jan 18 2009

			Concatenation of prime 2 and second prime 3 is the prime 23, hence 2 is in the sequence.
Concatenation of prime 23 and 23rd prime 83 is the prime 2383, hence 23 is in the sequence.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A045532, A155032 (resulting primes).

[ p: p in PrimesUpTo(3700) | IsPrime(StringToInteger(IntegerToString(p) cat IntegerToString(NthPrime(p)))) ];

A154963 = Select[ Prime[ Range[ 550 ] ], PrimeQ[ FromDigits[ Join[ IntegerDigits[ # ], IntegerDigits[ Prime[ # ] ] ] ] ] & ] (* Alonso del Arte Nov 12 2009 *)

Edited and extended beyond a(3) by Klaus Brockhaus, Jan 20 2009

A155088 Numbers n such that n and prime(n) contain prime digits only.

Original entry on oeis.org

2, 3, 55, 332, 352, 375, 733, 3573, 3575, 7235, 22222, 22223, 22322, 252323, 252335, 253777, 255225, 372755, 372772, 522532, 523255, 525737, 2275325, 2275327, 2275337, 2277333, 2277337, 3325772, 27727257, 27727277, 27727732, 27737332, 27737722, 27737723

Offset: 1

Juri-Stepan Gerasimov, Jan 20 2009

Indices n such that A045532(n) is in A046034. [R. J. Mathar, May 05 2010]

			352 is in the sequence since 352 and prime(352) = 2377 use only prime digits (2, 3, 5, 7). For more examples see Links.

Giovanni Resta, Table of n, a(n) for n = 1..200
Giovanni Resta, Table of a(n), prime(a(n)) for n = 1..200

Cf. A000027, A000040, A167483.

pQ[n_] := Union[IntegerDigits@n, {2,3,5,7}] == {2,3,5,7}; Select[Range[10^5], pQ@# && pQ@Prime@# &] (* Giovanni Resta, Mar 11 2013 *)
Select[Flatten[Table[FromDigits/@Tuples[{2,3,5,7},n],{n,8}]],AllTrue[ IntegerDigits[Prime[#]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jun 24 2015 *)

Corrected (332, 352, 375 inserted) by R. J. Mathar, May 05 2010

a(11)-a(34) from Giovanni Resta, Mar 11 2013

A191992 Concatenation of n and the n-th composite number.

Original entry on oeis.org

14, 26, 38, 49, 510, 612, 714, 815, 916, 1018, 1120, 1221, 1322, 1424, 1525, 1626, 1727, 1828, 1930, 2032, 2133, 2234, 2335, 2436, 2538, 2639, 2740, 2842, 2944, 3045, 3146, 3248, 3349, 3450, 3551, 3652, 3754, 3855, 3956, 4057, 4158, 4260, 4362, 4463, 4564, 4665, 4766, 4868, 4969, 5070, 5172, 5274, 5375, 5476

Offset: 1

Kausthub Gudipati, Jun 20 2011

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf. A045532, the prime analog of this sequence.

Cf. A246801, primes in this sequence.

Module[{upto=55,cmps,len},cmps=Select[Range[10*upto],CompositeQ];len= Min[ Length[ cmps],upto];#[[1]]*10^IntegerLength[#[[2]]]+#[[2]]&/@ Thread[{ Range[ len],Take[cmps,len]}]] (* Harvey P. Dale, Dec 05 2016 *)

n=0;for(k=4,1e3,if(isprime(k),k++);print1(n++k", ")) \\ Charles R Greathouse IV, Jun 21 2011

A253910 Concatenation of n-th prime and n-th nonprime.

Original entry on oeis.org

21, 34, 56, 78, 119, 1310, 1712, 1914, 2315, 2916, 3118, 3720, 4121, 4322, 4724, 5325, 5926, 6127, 6728, 7130, 7332, 7933, 8334, 8935, 9736, 10138, 10339, 10740, 10942, 11344, 12745, 13146, 13748, 13949, 14950, 15151, 15752, 16354, 16755, 17356, 17957, 18158, 19160, 19362, 19763, 19964, 21165, 22366, 22768, 22969

Offset: 1

Omar E. Pol, Feb 06 2015

Concatenate A000040(n) and A018252(n).

			a(5) = 119 because the 5th prime is 11 and the 5th nonprime is 9.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A018252, A038530, A045532, A075110, A106582, A138821, A138822, A253911.

import Data.Function (on)
a253911 n = a253911_list !! (n-1)
a253911_list = map read $
   zipWith ((++) `on` show) a018252_list a000040_list :: [Integer]
-- Reinhard Zumkeller, Feb 09 2015

nprime(n)=c=0;k=1;while(k,if(!isprime(k),c++);if(c==n,return(k));k++)
vector(50,n,eval(concat(Str(prime(n)),Str(nprime(n))))) \\ Derek Orr, Feb 06 2015

A253911 Concatenation of n-th nonprime and n-th prime.

Original entry on oeis.org

12, 43, 65, 87, 911, 1013, 1217, 1419, 1523, 1629, 1831, 2037, 2141, 2243, 2447, 2553, 2659, 2761, 2867, 3071, 3273, 3379, 3483, 3589, 3697, 38101, 39103, 40107, 42109, 44113, 45127, 46131, 48137, 49139, 50149, 51151, 52157, 54163, 55167, 56173, 57179, 58181, 60191, 62193, 63197, 64199, 65211, 66223, 68227, 69229

Offset: 1

Omar E. Pol, Feb 06 2015

Concatenate A018252(n) and A000040(n).

			a(5) = 911 because the 5th nonprime is 9 and the 5th prime is 11.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Cf. A000040, A018252, A038530, A045532, A075110, A106582, A138821, A138822, A253910.

import Data.Function (on)
a253911 n = a253911_list !! (n-1)
a253911_list = map read $
   zipWith ((++) `on` show) a018252_list a000040_list :: [Integer]
-- Reinhard Zumkeller, Feb 09 2015

cncat[{a_,b_}]:=FromDigits[Flatten[IntegerDigits/@{a,b}]]; Module[ {nn=100,np,len},np = Select[Range[nn],!PrimeQ[#]&];len=Length[np];cncat/@Thread[{np,Prime[Range[len]]}]] (* Harvey P. Dale, Oct 17 2020 *)

nprime(n)=c=0; k=1; while(k, if(!isprime(k), c++); if(c==n, return(k)); k++)
vector(50, n, eval(concat(Str(nprime(n)), Str(prime(n))))) \\ Derek Orr, Feb 06 2015

cp's OEIS Frontend

A075110 Concatenation of n-th prime and n in decimal notation.

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A138821 Concatenation of n-th Fibonacci number and n-th prime.

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Magma

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A138822 Concatenation of n-th prime and n-th Fibonacci number.

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Magma

Mathematica

A085451 Numbers n such that n and prime[n] together use only distinct digits.

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Mathematica

A139114 Concatenation of n-th Fibonacci number and n.

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Mathematica

A154963 Primes p such that the concatenation of p and prime(p) is prime.

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Magma

Mathematica

Extensions

A155088 Numbers n such that n and prime(n) contain prime digits only.

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Programs

Mathematica

Extensions

A191992 Concatenation of n and the n-th composite number.

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