A083758 -id:A083758 - cp's OEIS frontend

A338072 Concatenation of the digits of A083758.

2, 3, 1, 1, 7, 4, 1, 3, 1, 1, 7, 1, 6, 3, 2, 3, 7, 9, 1, 9, 7, 2, 4, 1, 2, 9, 3, 7, 5, 9, 1, 9, 3, 2, 2, 7, 2, 2, 9, 2, 3, 9, 4, 3, 9, 9, 2, 9, 3, 3, 7, 2, 5, 7, 1, 4, 4, 7, 5, 0, 9, 1, 9, 2, 9, 3, 1, 7, 2, 3, 1, 6, 1, 9, 9, 3, 7, 1, 7, 9, 3, 6, 7, 2, 5, 1, 1, 0, 6, 3, 4, 2, 4, 1

Offset: 1

N. J. A. Sloane, Oct 20 2020

This is the beginning of the decimal expansion of the very large primes defined in A083758 and A083759, read from left to right.

			The primes are:
2,
23,
2311,
23117,
2311741,
231174131,
23117413117,
23117413117163,
2311741311716323,
...
23117413117163237919724129
...
2311741311716323791972412937591932272292394399293372571447509192931723161993717936725110634241
...

Cf. A033308 (the Copeland-Erdős constant), A083758, A083759, A338073.

A083759 Primes arising in A083758.

Original entry on oeis.org

2, 23, 2311, 23117, 2311741, 231174131, 23117413117, 23117413117163, 2311741311716323, 231174131171632379, 231174131171632379197, 231174131171632379197241, 23117413117163237919724129

Offset: 1

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 06 2003

Cf. A083758, A338072.

More terms from Sean A. Irvine, Dec 15 2009

A338073 Rearrangement of positive integers except 3 defined by A083758.

Original entry on oeis.org

1, 2, 5, 4, 13, 11, 7, 38, 9, 22, 45, 53, 10, 12, 17, 44, 49, 50, 52, 85, 158, 68, 55, 229, 97, 8, 62, 269, 256, 159, 41, 73, 54, 179, 581, 210, 98, 297, 86, 34, 43, 273, 199, 122, 16, 153, 140, 29, 709, 521, 64, 163, 87, 389, 1145, 106, 164, 231, 26, 177, 28, 464, 51, 258, 398, 391

Offset: 1

N. J. A. Sloane, Oct 20 2020

nonn

This is conjectured to be a permutation of all positive integers except 3.

Apply PrimePi (A000720) to the terms of A083758.

Cf. A000720, A083758, A083759, A338072.

a338073(m)={my(np=1000*m,pused=vectorsmall(np),digp=[]);for(n=1,m,my(found=0);for(k=1,np, if(!pused[k],my(add=digits(prime(k)),pc=concat(digp,add));if(ispseudoprime(fromdigits(pc)),print1(k,", ");digp=pc;pused[k]=1;found=1;break)));if(!found,break))};
a338073(66) \\ Hugo Pfoertner, Oct 21 2020

A051670 Smallest prime that concatenated with all previous terms of sequence forms a prime.

Original entry on oeis.org

2, 3, 3, 3, 3, 23, 7, 3, 53, 19, 149, 571, 3, 131, 3, 151, 389, 31, 389, 97, 59, 277, 491, 181, 59, 67, 647, 1117, 797, 433, 41, 367, 29, 487, 719, 283, 347, 97, 1103, 193, 821, 13, 29, 31, 947, 619, 167, 229, 479, 271, 1217, 79, 2777, 241, 1361, 751, 83, 4603, 317

Offset: 1

Felice Russo, Dec 15 1999

			The 6th term of the sequence is 23 because that is smallest prime that when concatenated with previous terms 2, 3, 3, 3, 3, produces a prime (2333323).

A. Murthy, Smar. Notions J. Vol. 11, N. 1-2-3 Spring 2000

Paul Zimmermann, Table of n, a(n) for n = 1..1127 [First 200 terms from T. D. Noe]

Cf. A048549 and A083758.

nxt[{lst_,n_}]:=Module[{id=IntegerDigits[lst],np=2},While[ !PrimeQ[ FromDigits[ Join[id, IntegerDigits[np]]]],np=NextPrime[np]];{FromDigits[ Join[id,IntegerDigits[np]]],np}]; Transpose[NestList[nxt,{2,2},60]] [[2]] (* Harvey P. Dale, May 25 2015 *)
nxt[{l_,a_}]:=Module[{k=2},While[CompositeQ[l*10^IntegerLength[k]+ k],k= NextPrime[ k]];{l*10^IntegerLength[k]+k,k}]; NestList[nxt,{2,2},60][[All,2]] (* Harvey P. Dale, Aug 09 2020 *)

Extended by T. D. Noe, May 01 2010

A049462 a(n) is the smallest n-digit prime p such that the concatenation a(1)a(2)...a(n-1)p is prime, with a(1) = 2.

Original entry on oeis.org

2, 11, 151, 1013, 10867, 100673, 1000357, 10000931, 100000213, 1000000901, 10000001797, 100000000283, 1000000001911, 10000000012553, 100000000006087, 1000000000011317, 10000000000003471, 100000000000017431

Offset: 1

Jeff Heleen, Oct 13 2003

The corresponding primes are certified for 44 < n < 60 (for the first 15 titanic primes). - Metin Sariyar, Oct 23 2020

			Starting with an initial prime of 2, next the smallest 2-digit prime which gives a prime is 11 (211, a prime), then 151 (3-digit prime) is the smallest to make 211151 a prime, etc.

Metin Sariyar, Table of n, a(n) for n = 1..100

Cf. A080155, A083758.

NextPrim[n_] := Block[{k = n + 1}, While[ ! PrimeQ[k], k++ ]; k]; a[1] = 2; a[n_] := a[n] = Block[{p = Sum[ a[i]*10^(n(n + 1)/2 - i(i + 1)/2), {i, 1, n - 1}], q = NextPrim[10^(n - 1)]}, While[ !PrimeQ[p + q], q = NextPrim[q]]; q]; Table[ a[n], {n, 1, 19}] (* Robert G. Wilson v, Oct 18 2003 *)

More terms from Robert G. Wilson v, Oct 18 2003

cp's OEIS Frontend

A338072 Concatenation of the digits of A083758.

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A083759 Primes arising in A083758.

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A338073 Rearrangement of positive integers except 3 defined by A083758.

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A051670 Smallest prime that concatenated with all previous terms of sequence forms a prime.

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A049462 a(n) is the smallest n-digit prime p such that the concatenation a(1)a(2)...a(n-1)p is prime, with a(1) = 2.

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