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 1-3 of 3 results.

A080154 Values of n corresponding to the terms in sequence A080153.

Original entry on oeis.org

1, 2, 5, 9, 11, 13, 17, 22, 25, 28, 30, 36, 38, 41, 45, 48, 49, 53, 55, 58, 68, 76, 84, 85, 91, 94, 101, 114, 137, 139, 147, 153, 154, 156, 163, 165, 180, 189, 195, 200, 210, 211, 223, 235, 237, 241, 246, 247, 249, 253, 256, 272, 274, 286, 289, 293, 296, 306, 321, 323
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003

Keywords

Examples

			E.g. the first three terms are 1, 2 and 5 because the concatenation of the first, 2nd and 11th primes is 2311 and this is prime. Also, the 5th prime is the first one after 3 for which this concatenation is prime.

Crossrefs

Cf. A000720, A073640, A080153.

Programs

  • Maple
    with(numtheory): pout := [2,3]: nout := [1,2]: for n from 3 to 600 do: p := ithprime(n): d := parse(cat(pout[nops(pout)-1],pout[nops(pout)],p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: nout;

Formula

For each term a(n) in this sequence, A080153(n) = prime(a(n)).
a(n) = A000720(A080153(n)). - Sean A. Irvine, Sep 05 2025

Extensions

Edited by Charles R Greathouse IV, Apr 30 2010

A080155 a(1)=2; a(n) for n>1 is the smallest prime number > a(n-1) such that the concatenation of all previous terms is also prime.

Original entry on oeis.org

2, 3, 11, 31, 47, 229, 251, 577, 857, 859, 911, 1123, 1223, 1297, 1571, 2161, 2417, 2551, 2879, 3319, 5273, 6121, 6947, 7603, 8273, 12721, 12953, 13291, 15683, 16453, 17207, 18133, 20399, 23743, 23909, 25849, 28277, 28879, 35291, 35461, 36107, 43573
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003

Keywords

Comments

See A073640 for the sequence involving concatenation of 2 successive terms, A080153 for 3 successive terms. Primeness is established using Maple's isprime() function, so later terms should be regarded as "probable".

Examples

			E.g. a(5)=47 since this is the smallest prime>a(4) which, when concatenated with the concatenation of a(1) to a(4) (=231131), also yields a prime, in this case 23113147.

Links

Crossrefs

Cf. A073640, A080152, A080153, A080154, A080156.
Cf. A033679, A069603, A074338.

Programs

  • Maple
    with(numtheory): pout := [2]: nout := [1]: for n from 2 to 5000 do: p := ithprime(n): d := parse(cat(seq(pout[i],i=1..nops(pout)),p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: pout;
  • Mathematica
    f[s_List] := Block[{p=NextPrime@s[[-1]], pp=FromDigits@Flatten[IntegerDigits/@s]}, While[!PrimeQ[pp*10^Floor[Log[10,p]+1]+p], p=NextPrime@p]; Append[s,p]]; Nest[f,{2},40]

Formula

For any n>1, a(n) is prime and a(n) > a(n-1). a(n) is the smallest prime for which a(1)//a(2)//...//a(n) is prime. // denotes concatenation.

A080156 Values of n corresponding to the terms in sequence A080155. For any k, the concatenation of the a(1) to a(k)-th primes is prime and each value of k is the smallest for which this is true.

Original entry on oeis.org

1, 2, 5, 11, 15, 50, 54, 106, 148, 149, 156, 188, 200, 211, 248, 326, 359, 374, 417, 467, 699, 798, 891, 966, 1038, 1519, 1542, 1578, 1831, 1908, 1982, 2079, 2305, 2640, 2660, 2845, 3078, 3145, 3760, 3777, 3835, 4538, 4630, 4991, 5019, 5554, 5658, 5827
Offset: 1

Views

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 31 2003

Keywords

Links

Crossrefs

Cf. A000720, A073640, A080152, A080153, A080154, A080155.

Programs

  • Maple
    with(numtheory): pout := [2]: nout := [1]: for n from 2 to 5000 do: p := ithprime(n): d := parse(cat(seq(pout[i],i=1..nops(pout)),p)): if (isprime(d)) then pout := [op(pout),p]: nout := [op(nout),n]: fi: od: nout;

Formula

a(n) = primepi(A080155(n)) = A000720(A080155(n)).

Extensions

Edited by Charles R Greathouse IV, Apr 30 2010
Showing 1-3 of 3 results.

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