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.

A007512 Primes of the form floor(e*10^k), i.e., formed by concatenation of an initial segment of the decimal expansion of e.

Original entry on oeis.org

2, 271, 2718281, 2718281828459045235360287471352662497757247093699959574966967627724076630353547594571
Offset: 1

Views

Author

N. J. A. Sloane, Robert G. Wilson v, Simon Plouffe

Keywords

Comments

The number of digits in a(n) is given in A064118. This allows us to get larger terms that cannot be displayed here, via the given FORMULA. Sequences A005042, A072952, A115453, A119343, A210704, ... are the analogs for Pi, gamma, sqrt(2), sqrt(3), 3^(1/3), ... - M. F. Hasler, Aug 31 2013

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Programs

  • Maple
    Digits := 110; n0 := evalf(E); for i from 1 to 100 do t1 := trunc(10^i*n0); if isprime(t1) then print(t1); fi; od:
  • PARI
    c=exp(1);for(k=0,precision(c),ispseudoprime(c\.1^k) & print1(c\.1^k,",")) \\ M. F. Hasler, Sep 01 2013

Formula

a(n) = floor(e*10^(A064118(n)-1)). - M. F. Hasler, Aug 31 2013

Extensions

Next term is a 1781-digit BPSW-probable prime 2718281828459045235...211151368350627526023. - Randall L Rathbun, Feb 02 2002
Edited by T. D. Noe, Oct 30 2008
Edited by M. F. Hasler, Aug 31 2013

A186734 Triangular array C(n,k) counting connected k-regular simple graphs on n vertices with girth exactly 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 5, 2, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 20, 12, 1, 1, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 101, 220, 7, 1, 1, 0, 0, 0, 0, 1606, 0, 1, 0, 0, 0, 0, 743, 16828, 388, 9, 1, 1, 0, 0, 0, 0, 193900, 0, 6, 0, 0, 0, 0, 0, 7350
Offset: 1

Views

Author

Jason Kimberley, Mar 20 2013

Keywords

Comments

In the n-th row 0 <= 2k <= n.

Examples

			01: 0;
02: 0, 0;
03: 0, 0;
04: 0, 0, 1;
05: 0, 0, 0;
06: 0, 0, 0, 1;
07: 0, 0, 0, 0;
08: 0, 0, 0, 2, 1;
09: 0, 0, 0, 0, 0;
10: 0, 0, 0, 5, 2, 1;
11: 0, 0, 0, 0, 2, 0;
12: 0, 0, 0, 20, 12, 1, 1;
13: 0, 0, 0, 0, 31, 0, 0;
14: 0, 0, 0, 101, 220, 7, 1, 1;
15: 0, 0, 0, 0, 1606, 0, 1, 0;
16: 0, 0, 0, 743, 16828, 388, 9, 1, 1;
17: 0, 0, 0, 0, 193900, 0, 6, 0, 0;
18: 0, 0, 0, 7350, 2452818, 406824, 267, 8, 1, 1;
19: 0, 0, 0, 0, 32670329, 0, 3727, 0, 0, 0;
20: 0, 0, 0, 91763, 456028472, 1125022325, 483012, 741, 13, 1, 1;
21: 0, 0, 0, 0, 6636066091, 0, 69823723, 0, 1, 0, 0;

Links

Crossrefs

The sum of the n-th row of this sequence is A186744(n).
Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *exactly* g: A186733 (g=3), this sequence (g=4).
Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth *at least* g: A068934 (g=3), A186714 (g=4).

Formula

C(n,k) = A186714(n,k) - A186715(n,k), noting the differing row lengths.
E(n,k) = A185644(n,k) - A210704(n,k), noting the differing row lengths.

A185644 Triangular array E(n,k) counting, not necessarily connected, k-regular simple graphs on n vertices with girth exactly 4.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 5, 2, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 21, 12, 1, 1, 0, 0, 2, 0, 31, 0, 0, 0, 0, 3, 103, 220, 7, 1, 1, 0, 0, 3, 0, 1606, 0, 1, 0, 0, 0, 5, 752, 16829, 388, 9, 1, 1, 0, 0, 5, 0, 193900, 0, 6, 0, 0, 0
Offset: 1

Views

Author

Jason Kimberley, Feb 22 2013

Keywords

Comments

In the n-th row 0 <= 2k <= n.

Examples

			01: 0;
02: 0, 0;
03: 0, 0;
04: 0, 0, 1;
05: 0, 0, 0;
06: 0, 0, 0, 1;
07: 0, 0, 0, 0;
08: 0, 0, 1, 2, 1;
09: 0, 0, 1, 0, 0;
10: 0, 0, 0, 5, 2, 1;
11: 0, 0, 1, 0, 2, 0;
12: 0, 0, 2, 21, 12, 1, 1;
13: 0, 0, 2, 0, 31, 0, 0;
14: 0, 0, 3, 103, 220, 7, 1, 1;
15: 0, 0, 3, 0, 1606, 0, 1, 0;
16: 0, 0, 5, 752, 16829, 388, 9, 1, 1;
17: 0, 0, 5, 0, 193900, 0, 6, 0, 0;
18: 0, 0, 7, 7385, 2452820, 406824, 267, 8, 1, 1;
19: 0, 0, 8, 0, 32670331, 0, 3727, 0, 0, 0;
20: 0, 0, 11, 91939, 456028487, 1125022326, 483012, 741, 13, 1, 1;
21: 0, 0, 12, 0, 6636066126, 0, 69823723, 0, 1, 0, 0;
22: 0, 0, 16, 1345933, 100135577863, 3813549359275, 14836130862, 2887493, ?, 14, 1;

Links

Crossrefs

The sum of the n-th row of this sequence is A198314(n).
Not necessarily connected k-regular simple graphs girth exactly 4: A198314 (any k), this sequence (triangle); fixed k: A026797 (k=2), A185134 (k=3), A185144 (k=4).

Formula

E(n,k) = A186734(n,k) + A210704(n,k), noting the differing row lengths.
E(n,k) = A185304(n,k) - A185305(n,k), noting the differing row lengths.

A072952 Primes obtained as initial segments of the decimal expansion of the Euler-Mascheroni constant gamma = 0.5772... .

Original entry on oeis.org

5, 577, 5772156649015328606065120900824024310421
Offset: 1

Views

Author

Shyam Sunder Gupta, Aug 12 2002

Keywords

Comments

The next term (a(4)) has 185 digits and is too large to include. - Harvey P. Dale, May 14 2013
Sequence A065815 gives the number of digits of a(n), resp. numbers k such that a(n) = floor(gamma*10^k). Sequences A005042, A007512, A115453, A119343, A210704, ... are the analog of the present sequence for Pi, e, sqrt(2), sqrt(3), 3^(1/3), ... - M. F. Hasler, Aug 31 2013
The original wording of the definition (and example) was "primes found in the decimal expansion..." which could as well refer to the sequence (5,7,7,215664901,5,3,2, ...) or (5,7,72156649, ...) or (5,7,7215664901, ...) (analogs to A047777 or A195834), or to the sequence (5,7,57, ...), analog to A198018. - M. F. Hasler, Sep 01 2013

Examples

			a(2) = 577, since 577 is the second prime obtained as initial segment of the decimal expansion of Euler-Mascheroni constant gamma = 0.577215664... .

Links

Crossrefs

Cf. A001620, A047777, A065815, A195834, A198018.
Analogous sequences: A005042 (Pi), A007512 (e), A115453 (sqrt(2)), A119343 (sqrt(3)), A210704 (3^(1/3)).

Programs

  • Mathematica
    nn=200;With[{emc=RealDigits[EulerGamma,10,nn][[1]]},Select[Table[ FromDigits[ Take[emc,n]],{n,nn}],PrimeQ]] (* Harvey P. Dale, May 14 2013 *)
  • PARI
    default(realprecision, 777); /* use that many digits */
A072952={(c=Euler, v=1/*set to 0 for indices (i.e., A065815) instead of values*/)->for(k=0, precision(c), ispseudoprime(p=c\.1^k)&&print1([k, p][1+v]", "))} \\ M. F. Hasler, Aug 31 2013

A210706 Numbers k such that floor[ 3^(1/3)*10^k ] is prime.

Original entry on oeis.org

23, 80, 2487
Offset: 1

Views

Author

M. F. Hasler, Aug 31 2013

Keywords

Comments

Inspired by prime curios about 4957 (cf. LINKS), one of which honors the late Bruce Murray (Nov 30 1931 - Aug 29 2013).
Meant to be a "condensed" version of A210704, see there for more.
Alternate definition: Numbers k such that concatenation of the first (k+1) digits of A002581 yields a prime.

Examples

			t = 3^(1/3) = 1.44224957030740838232163831... multiplied by 10^23 yields
t*10^23 = 144224957030740838232163.831..., the integer part of which is the prime A210704(1), therefore a(1)=23.

Links

Crossrefs

Cf. A002581 = decimal expansion of 3^(1/3).
Cf. A065815 (analog for gamma), A060421 (1+ analog for Pi), A064118 (1+ analog for exp(1)), A119344 (1 + analog for sqrt(3)), A136583 (1+ analog for sqrt(10)).

Programs

  • PARI
    \p2999
t=sqrtn(3,3);for(i=1,2999,ispseudoprime(t\.1^i)&print1(i","))

Formula

a(n) = (length of A210704(n)) - 1, where "length" means number of decimal digits.
Showing 1-5 of 5 results.

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

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