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 1-5 of 5 results.

A153050 Six-digit squares that are concatenation of two 3-digit primes.

Original entry on oeis.org

101761, 113569, 127449, 131769, 137641, 149769, 167281, 199809, 349281, 439569, 463761, 491401, 641601, 683929, 797449
Offset: 1

Views

Author

Zak Seidov, Dec 17 2008

Keywords

Comments

a(n)=(A153048(n))^2.
There are exactly 15 such numbers.

Crossrefs

Cf. A153048.

Programs

  • Mathematica
    c = 0; t = 1000; re = Sort[Reap[Do[If[PrimeQ[p], Do[If[PrimeQ[q], r = p*t + q; s = Sqrt[r]; If[s == Floor[s], c++; Sow[r]]], {q, 101, 999, 2}]], {p, 101, 999, 2}]][[2, 1]]]
concatpQ[n_]:=Module[{idn=IntegerDigits[n],a,b},a=FromDigits[Take[idn,3]];b=FromDigits[Take[idn,-3]];IntegerLength[a]==IntegerLength[b]==3 && PrimeQ[a]&&PrimeQ[b]]; Select[Range[316,1000]^2,concatpQ] (* Harvey P. Dale, Mar 09 2012 *)

A248046 Primes p such that p^2 is the concatenation of two k-digit primes where k is half the length of p^2.

Original entry on oeis.org

5, 73, 337, 409, 701, 827, 5449, 5477, 5939, 6841, 7417, 8353, 8573, 9109, 9227, 9311, 9733, 9767, 32569, 34319, 34327, 34501, 35933, 35999, 38371, 38449, 38923, 38953, 39023, 39367, 39671, 40531, 40973, 42701, 43543, 44651, 45259, 46021, 47623, 48311, 49531, 50923, 54133, 54437, 54547
Offset: 1

Views

Author

Derek Orr, Oct 03 2014

Keywords

Examples

			73 is prime, and 73^2 = 5329 is the concatenation of two 2-digit primes (53 and 29). So 73 is a member of this sequence.
929 is not in the sequence since 929^2 = 863041, where 863 is a 3-digit prime but 041 is a 2-digit prime. - _Jens Kruse Andersen_, Oct 06 2014

Links

Crossrefs

Cf. A105184, A030461, A153048, A153164, A080906, A248208.

Programs

  • PARI
    forprime(p=1,10^5,d=digits(p^2);if((#d)%2==0,if(isprime((p^2)\(10^(#d/2)))&&isprime((p^2)%(10^(#d/2)))&&#Str((p^2)%(10^(#d/2)))==#d/2,print1(p,", "))))

Extensions

Terms and program corrected by Derek Orr to match definition, thanks to Jens Kruse Andersen

A248208 Primes p such that p^3 is the concatenation of two k-digit primes where k is half the number of decimal digits in p^3.

Original entry on oeis.org

3, 11, 47, 83, 1063, 1637, 1699, 7529, 7673, 23059, 28097, 29573, 34157, 34961, 36587, 40897, 43609, 44711, 101839, 102763, 103423, 104087, 104393, 106363, 117437, 117499, 124471, 125407, 126011, 129419, 134753, 135007, 137393, 139487, 143879, 143971, 145037
Offset: 1

Views

Author

Derek Orr, Oct 03 2014

Keywords

Examples

			47 is prime and 47^3 = 103823 is the concatenation of two primes (103 and 823) that are of the same length (here, their length is 3). So, 47 is a member of this sequence.
73 is not in the sequence since 73^3 = 389017, where 389 is a 3-digit prime but 017 is a 2-digit prime. - _Jens Kruse Andersen_, Oct 06 2014

Links

Crossrefs

Cf. A030078, A105184, A030461, A153048, A080906, A248046.

Programs

  • PARI
    forprime(p=1,10^6,d=digits(p^3);if((#d)%2==0,if(isprime((p^3)\(10^(#d/2)))&&isprime((p^3)%(10^(#d/2)))&&#Str((p^3)%(10^(#d/2)))==#d/2,print1(p,", "))))

Extensions

Terms and PARI program corrected by Jens Kruse Andersen, Oct 06 2014

A153139 Numbers n with property that n^2 is a concatenation of three 3-digit primes.

Original entry on oeis.org

10171, 10371, 10447, 10449, 10451, 11303, 11801, 11827, 12319, 12553, 13387, 13829, 13847, 13903, 13913, 14141, 14549, 15087, 15097, 15153, 15847, 16431, 16841, 16847, 17549, 18363, 18379, 18637, 18697, 18701, 19319, 19337, 19579
Offset: 1

Views

Author

Zak Seidov, Dec 19 2008

Keywords

Comments

There are exactly 60 such numbers.

Examples

			a(1)= 10171, 10171^2=103_449_241
a(2)= 10371, 10371^2=107_557_641
a(60)=31591, 31591^2=997_991_281

Links

Crossrefs

Cf. A153048, A153050

Programs

  • Mathematica
    ttdpQ[n_]:=Module[{c=FromDigits/@Partition[IntegerDigits[n^2],3]}, Min[ IntegerLength[ c]] ==3&&AllTrue[c,PrimeQ]]; Select[Range[ 10000,31622], ttdpQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 26 2016 *)

A153164 Primes p with property that p^2 is a concatenation of two 3-digit primes.

Original entry on oeis.org

337, 409, 701, 827
Offset: 1

Views

Author

Zak Seidov, Dec 20 2008

Keywords

Comments

There are exactly 4 such numbers.

Examples

			{337,409,701,827}^2 ={113_569, 167_281, 491_401, 683_929}.

Crossrefs

Cf. A153048, A153050.

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010
Showing 1-5 of 5 results.

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