A083759 -id:A083759 - cp's OEIS frontend

A083758 Lexicographically earliest infinite sequence of distinct primes such that the concatenation of the initial n terms is a prime for all n >= 1.

2, 3, 11, 7, 41, 31, 17, 163, 23, 79, 197, 241, 29, 37, 59, 193, 227, 229, 239, 439, 929, 337, 257, 1447, 509, 19, 293, 1723, 1619, 937, 179, 367, 251, 1063, 4241, 1291, 521, 1951, 443, 139, 191, 1753, 1217, 673, 53, 883, 809, 109, 5381, 3733, 311, 967, 449

Offset: 1

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

Conjecture: every prime except 5 is a term.

However, after 1000 terms, 13, 47, 61, ... are still missing. A158521 suggests there is no intrinsic reason why 13 should not eventually appear. - N. J. A. Sloane, Oct 21 2020

			2 is a prime.
2||3 = 23 is a prime.
2||3||7 = 3*79 but 2||3||11 = 2311 is a prime
So is 23117.  And so on.

Paul Zimmermann, Table of n, a(n) for n = 1..1479 [First 800 terms from Giorgos Kalogeropoulos; first 1156 terms from Metin Sariyar]

Cf. A051670, A083759, A338072, A338073, A051670.

A338072 Concatenation of the digits of A083758.

Original entry on oeis.org

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.

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

cp's OEIS Frontend

A083758 Lexicographically earliest infinite sequence of distinct primes such that the concatenation of the initial n terms is a prime for all n >= 1.

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A338072 Concatenation of the digits of A083758.

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A338073 Rearrangement of positive integers except 3 defined by A083758.

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