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.

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A212525 Primes containing a digit 3.

Original entry on oeis.org

3, 13, 23, 31, 37, 43, 53, 73, 83, 103, 113, 131, 137, 139, 163, 173, 193, 223, 233, 239, 263, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 431, 433, 439, 443, 463, 503, 523, 563, 593, 613, 631, 643, 653, 673, 683
Offset: 1

Views

Author

Jaroslav Krizek, Jun 12 2012

Keywords

Comments

Supersequence of A045709, A106103 and A106099. Subsequence of A011533 and A062667.

Links

Crossrefs

Cf. A045709 (primes with first digit 3), A011533 (numbers containing a digit 3), A062667 (numbers n such that every divisor of n (except 1) contains the digit 3), A106099 (primes with maximal digit = 3), A106103 (primes with minimal digit = 3), A038611 (primes not containing digit 3).

Programs

  • Mathematica
    Select[Prime[Range[200]], MemberQ[IntegerDigits[#], 3] &] (* T. D. Noe, Jun 12 2012 *)

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Nov 01 2022

A062333 Primes starting and ending with 3.

Original entry on oeis.org

3, 313, 353, 373, 383, 3023, 3083, 3163, 3203, 3253, 3313, 3323, 3343, 3373, 3413, 3433, 3463, 3533, 3583, 3593, 3613, 3623, 3643, 3673, 3733, 3793, 3803, 3823, 3833, 3853, 3863, 3923, 3943, 30013, 30103, 30113, 30133, 30203, 30223, 30253, 30293
Offset: 1

Views

Author

Amarnath Murthy, Jun 21 2001

Keywords

Comments

Intersection of A045709 and A030431. - Michel Marcus, Jun 08 2013

Examples

			3413 is a member, as it is a prime and the first and the last digits are both 3.

Links

Crossrefs

Cf. A062332, A062334, A062335.

Programs

  • Mathematica
    se3Q[n_]:=Module[{idn=IntegerDigits[n]},idn[[1]]==idn[[-1]]==3]; Select[ Prime[ Range[3300]],se3Q] (* Harvey P. Dale, Jul 24 2019 *)
  • PARI
    { n=-1; t=log(10); forprime (p=2, 5*10^5, if ((p-10*(p\10)) == 3 && (p\10^(log(p)\t)) == 3, write("b062333.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 05 2009

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 29 2001
Offset changed by Andrew Howroyd, Sep 17 2024

A065682 Number of primes <= prime(n) which begin with a 3.

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19
Offset: 1

Views

Author

Reinhard Zumkeller, Nov 13 2001

Keywords

Examples

			a(1) = 0, a(2) = 1. a(664579) = 75290 (A000040(664579) = 9999991 is the largest prime < 10^7).

Links

Crossrefs

Cf. A000040, A045709, A065680.

Programs

  • Mathematica
    Accumulate@ Array[Boole[First@ IntegerDigits@ Prime@ # == 3] &, 87] (* Michael De Vlieger, Jun 14 2018 *)
  • PARI
    lista(n) = { my(a=[p\10^logint(p,10)==3 | p<-primes(n)]); for(i=2, #a, a[i]+=a[i-1]); a} \\ Harry J. Smith, Oct 26 2009
Previous Showing 21-23 of 23 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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