A100003 -id:A100003 - cp's OEIS frontend

A089923 Duplicate of A100003.

5, 17, 89, 383

Offset: 5

Cino Hilliard, Jan 11 2004

dead

Previous name: Largest prime in the reverse concatenation of the first n consecutive prime numbers when that concatenation is a prime.

			53 is the reverse concatenation of the consecutive primes 3 and 5. 53 is prime.

revprime2(n) = { y=3; forprime(x=5,n, y=concat(Str(x),Str(y)); z=eval(y); if(ispseudoprime(z),print(x","z)) ) }

Edited by T. D. Noe, Oct 30 2008

A092447 Concatenate odd primes in decreasing order.

Original entry on oeis.org

3, 53, 753, 11753, 1311753, 171311753, 19171311753, 2319171311753, 292319171311753, 31292319171311753, 3731292319171311753, 413731292319171311753, 43413731292319171311753, 4743413731292319171311753, 534743413731292319171311753, 59534743413731292319171311753

Offset: 1

Micha Fleuren (michafleuren(AT)hotmail.com), Mar 24 2004

Andrew Howroyd, Table of n, a(n) for n = 1..100
M. Fleuren, Smarandache Back Concatenated Odd Primes
H. Marimutha, Smarandache Concatenated Type Sequences, Bulletin of Pure and Applied Sciences, Vol. 16 E(No.2), 1997; p. 225-226.
F. Smarandache, Collected papers, Vol. II, University of Kishinev, 1997.

Primes in A092448 and their corresponding starting value in A100003. [Dmitry Kamenetsky, Mar 02 2009]

Cf. A065091 (odd primes).

Table[FromDigits[Flatten[IntegerDigits/@Reverse[Prime[Range[2,n]]]]],{n,2,21}] (* Harvey P. Dale, Mar 01 2023 *)

a(n)={fromdigits(concat([digits(k) | k<-Vecrev(primes(n+1))[1..n]]))} \\ Andrew Howroyd, Feb 12 2020

More terms from Ray Chandler, Mar 28 2004
Offset corrected by Michel Marcus, Aug 15 2017
Terms a(14) and beyond from Andrew Howroyd, Feb 12 2020

A099071 Composite numbers k such that the concatenation of all nonprime positive integers up to k in decreasing order is prime.

Original entry on oeis.org

4, 6, 8, 9, 26, 1752

Offset: 1

Farideh Firoozbakht, Nov 06 2004

The terms of this sequence are composite terms of the sequence A099070 with the same order. Next term is greater than 6000 and the prime corresponding to the next term has more than 20000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 2, 3, 4, 5, 29, and 5010.

			26 is a term: 26 is composite; nonprimes up to 26 are 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26; and 26252422212018161514121098641 is prime.

Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles and Problems Connection.

Cf. A099070, A100003, A046284.

Do[If[ !PrimeQ[n]&&PrimeQ[(v={};Do[If[ !PrimeQ[n+1-j], v=Join[v, IntegerDigits[n+1-j]]], {j, n}];FromDigits[v])], Print[n]], {n, 6013}]
cnpQ[n_]:=PrimeQ[FromDigits[Flatten[IntegerDigits/@Select[Range[n,1,-1],!PrimeQ[#]&]]]]; Select[Range[1800],!PrimeQ[#]&&cnpQ[#]&] (* Harvey P. Dale, Jul 19 2020 *)

A092448 Primes in A092447.

Original entry on oeis.org

3, 53, 171311753, 8983797371676159534743413731292319171311753

Offset: 1

Micha Fleuren (michafleuren(AT)hotmail.com), Mar 24 2004

The next term, a(5), is too large to include. - Ray Chandler, Mar 28 2004

a(5), a(6) start with 383..., 8831...: cf. A100003. - M. F. Hasler, Apr 05 2008

M. Fleuren, Smarandache Back Concatenated Odd Primes
H. Marimutha, Smarandache Concatenated Type Sequences, Bulletin of Pure and Applied Sciences, Vol. 16 E(No.2), 1997; p. 225-226.
F. Smarandache, Collected papers, Vol. II, University of Kishinev, 1997.

Cf. A100003.

t="";forprime(p=3,9999,ispseudoprime(t=eval(Str(p,t)))&print(t)) \\\\ - M. F. Hasler, Apr 05 2008

More terms from Ray Chandler, Mar 28 2004

A099073 Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.

Original entry on oeis.org

2, 3, 7, 24, 76, 1100

Offset: 1

Farideh Firoozbakht, Nov 06 2004

A100003(n) = prime(a(n)). Next term is greater than 4500 and the prime corresponding to the next term has more than 21000 digits. Number of digits of primes corresponding to the six known terms of the sequence are respectively 1, 2, 9, 43, 198, and 4202. There is no known prime formed by concatenation of the first k odd primes in increasing order for 1 < k < 2250.

a(7) > 20000. - Michael S. Branicky, Nov 25 2024

			7 is in the sequence because the first 6 odd primes are 3,5,7,11,13,17 and 17.13.11.7.5.3 is prime (dot between numbers means concatenation).

Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles and Problems Connection.

Cf. A046035, A099070, A099071.

Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[n]], {n, 2, 4500}]
Select[Range[1100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Reverse[ Prime[ Range[ 2,#]]]]]]&] (* Harvey P. Dale, Nov 12 2017 *)

A164893 Base 10 representation of the string formed by appending primes in base 2.

Original entry on oeis.org

2, 11, 93, 751, 12027, 192445, 6158257, 197064243, 6306055799, 201793785597, 6457401139135, 413273672904677, 26449515065899369, 1692768964217559659, 108337213709923818223, 6933581677435124366325, 443749227355847959444859, 28399950550774269404471037

Offset: 1

Gil Broussard, Aug 29 2009

The subsequence of primes begins: 2, 11, 751. [Jonathan Vos Post, May 26 2010]

			The primes in base 2 (10, 11, 101, 111,...) concatenated by appending give the first four binary terms 10, 1011, 1011101, 1011101111; or 2, 11, 93, 751 base 10.

Charles R Greathouse IV, Table of n, a(n) for n = 1..335 (all terms under 1000 digits)

Cf. A000040, A004676, A007088, A100003, A154703.

nn=20;With[{b2p=IntegerDigits[#,2]&/@Prime[Range[nn]]},Table[ FromDigits[ Flatten[ Take[b2p,n]],2],{n,nn}]] (* Harvey P. Dale, Mar 26 2013 *)

list(n)=my(p=primes(n),s);vector(n,i,s=s<<#binary(p[i])+p[i]) \\ Charles R Greathouse IV, Mar 26 2013

a(n) = A154703(n) [converted from base 2 to base 10]. [Jonathan Vos Post, May 26 2010]

Corrected by Harvey P. Dale, Mar 26 2013

A178388 Concatenation of the first n primes written in base 3.

Original entry on oeis.org

2, 210, 21012, 2101221, 2101221102, 2101221102111, 2101221102111122, 2101221102111122201, 2101221102111122201212, 21012211021111222012121002, 210122110211112220121210021011, 2101221102111122201212100210111101

Offset: 1

Jonathan Vos Post, May 26 2010

			a(4) = Concatenate[prime(1) base 3, prime(2) base 3, prime(3) base 3, prime(3) base 3] = Concatenate[2 base 3, 3 base 3, 5 base 3, 7 base 3] = Concatenate[2, 10, 12, 21] = 2101221.

Rémy Sigrist, Table of n, a(n) for n = 1..174

Cf. A000040, A001363, A004676, A007088, A007089, A019518, A031974, A100003, A154703.

Module[{nn=15,p3},p3=IntegerDigits[Prime[Range[nn]],3];Table[FromDigits[Flatten[ Take[p3,n]]],{n,nn}]] (* Harvey P. Dale, Aug 25 2022 *)

v = 0; for (n=1, 12, d = digits(prime(n), 3); v = v*10^#d + fromdigits(d); print1 (v ", ")) \\ Rémy Sigrist, Aug 07 2017

Edited by N. J. A. Sloane, Jul 02 2017

cp's OEIS Frontend

A089923 Duplicate of A100003.

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A092447 Concatenate odd primes in decreasing order.

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A099071 Composite numbers k such that the concatenation of all nonprime positive integers up to k in decreasing order is prime.

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A092448 Primes in A092447.

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A099073 Numbers k such that the concatenation of the first k-1 odd primes in decreasing order is prime.

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A164893 Base 10 representation of the string formed by appending primes in base 2.

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A178388 Concatenation of the first n primes written in base 3.

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