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.

Previous Showing 31-40 of 203 results. Next

A144572 Primes of the form nonprime(prime(n))+1, where n-th nonprime = A141468(n) and first nonprime = 0.

Original entry on oeis.org

2, 5, 11, 17, 41, 59, 73, 83, 97, 127, 179, 191, 227, 283, 353, 389, 431, 461, 563, 571, 599, 661, 727, 751, 797, 877, 947, 1031, 1087, 1093, 1103, 1129, 1217, 1297, 1303, 1409, 1453, 1483, 1523, 1543, 1567, 1697, 1741, 1753, 1787, 1801, 1823, 1867, 1913
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 06 2009

Keywords

Extensions

Extended by Charles R Greathouse IV, Mar 29 2010

A151960 Sum_{x = A141468(n) to A000040(n)} 1-(-1)^x*x.

Original entry on oeis.org

2, 5, 3, 3, 6, 16, 12, 12, 15, 37, 24, 30, 33, 55, 39, 45, 77, 54, 88, 66, 66, 72, 109, 84, 129, 99, 99, 142, 105, 108, 126, 175, 138, 138, 200, 153, 211, 168, 171, 233, 186, 244, 201, 201, 204, 268, 222, 303, 243, 243, 316, 255, 255, 267, 349, 282
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jul 14 2009

Keywords

Examples

			a(1)=1-0+1+1+1-2=2, a(2)=1+1+1-2+1+3=5, a(3)=1-4+1+5=3, a(4)=1-6+1+7=3, a(5)=1-8+1+9+1-10+1+11=6, a(6)=1+9+1-10+1+11+1-12+1+13=16, a(7)=1-10+1+11+1-12+1+13+1-14+1+15+1-16+1+17=12, a(8)=1-12+1+13+1-14+1+15+1-16+1+17+1-18+1+19=12, a(9)=1-14+1+15+1-16+1+17+1-18+1+19+1-20+1+21+1-22+1+23=15, a(10)=1+15+1-16+1+17+1-18+1+19+1-20+1+21+1-22+1+23+1-24+1+25+1-26+1+27+1-28+1+29=37, ...

Crossrefs

Cf. A000040, A141468, A161669.

Programs

  • Mathematica
    ZeroAndNonPrime[n_Integer] := FixedPoint[n - 1 + PrimePi@# &, n - 1 + PrimePi@n]; ZeroAndNonPrime[2] = 1; f[n_] := Sum[1-(-1)^x*x, {x, ZeroAndNonPrime@n, Prime@n}]; Array[f, 56]

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jul 24 2009
Definition clarified by N. J. A. Sloane, Jul 25 2009
Definition corrected by Charles R Greathouse IV, Jul 22 2010

A154506 Primes of the form concatenation(A141468(k), k).

Original entry on oeis.org

43, 107, 149, 2719, 3323, 5641, 5843, 7253, 7757, 8059, 8563, 9067, 12697, 182141, 188147, 224177, 279221, 298237, 300239, 315251, 350281, 360289, 362291, 371299, 388313, 412333, 418339, 424343, 448363, 453367, 460373, 469379, 473383, 549449, 558457
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Jan 11 2009

Keywords

Examples

			43 is a term since 43 is a prime and A141468(3)=4.
107 is a term since 107 is a prime and A141468(7)=10.

Crossrefs

Cf. A141468.

Programs

  • Maple
    # read transforms; read b-file for A141468 (giving list b1); then:
t0:=[];
for n from 2 to nops(b1) do
t1:=cat(b1[n],n);
t2:=stoint(t1);
if isprime(t2) then t0:=[op(t0), t2]; fi;
od:
t0; # N. J. A. Sloane, Jun 27 2009

Extensions

Edited and extended from a(13) onwards by N. J. A. Sloane, Jun 26 2009

A156333 Odd nonprimes q=A141468(j) such that largest digit(j)+largest digit(q) is a prime.

Original entry on oeis.org

1, 39, 57, 91, 115, 121, 133, 143, 145, 147, 153, 155, 161, 175, 189, 203, 205, 207, 225, 231, 235, 243, 253, 255, 261, 273, 279, 285, 295, 299, 301, 303, 323, 325, 327, 341, 343, 345, 351, 355, 377, 385, 387, 411, 415, 427, 429, 441, 445, 447, 451, 465, 481, 483
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Feb 08 2009

Keywords

Comments

Subsequence of A014076 - R. J. Mathar, Feb 10 2009

Crossrefs

Cf. A000027, A000040, A141468.

Extensions

Rephrased definition. Inserted 207. - R. J. Mathar, Feb 10 2009

A157968 2^n - 1 (A000225) where n is nonprime number (A141468).

Original entry on oeis.org

0, 1, 15, 63, 127, 255, 511, 1023, 4095, 16383, 32767, 65535, 262143, 1048575, 2097151, 4194303, 16777215, 33554431, 67108863, 134217727, 268435455, 1073741823, 4294967295
Offset: 0

Views

Author

Jani Melik, Mar 10 2009

Keywords

Comments

a(0) = 0 since 2^0 - 1 = 0 and 0 is nonprime, a(1) = 1 since 2^1 - 1 = 1 and 1 is nonprime, a(2) = 15 since 2^4 - 1 = 15 and 4 is nonprime, ...

Crossrefs

A000668

A163638 Two copies of the sequence A141468, one at prime the other at nonprime indices.

Original entry on oeis.org

0, 1, 0, 1, 4, 4, 6, 6, 8, 9, 10, 8, 12, 9, 14, 15, 16, 10, 18, 12, 20, 21, 22, 14, 24, 25, 26, 27, 28, 15, 30, 16, 32, 33, 34, 35, 36, 18, 38, 39, 40, 20, 42, 21, 44, 45, 46, 22, 48, 49, 50, 51, 52, 24, 54, 55, 56, 57, 58, 25, 60, 26, 62, 63, 64, 65, 66, 27, 68, 69, 70, 28, 72, 30, 74, 75
Offset: 0

Views

Author

Juri-Stepan Gerasimov, Aug 02 2009

Keywords

Comments

The indices of this sequence are labeled as 0=N, 1=N, 2=P, 3=P, 4=N, 5=P, 6=N, etc. N=nonprime or P=prime. The numbers 0,1,4,6,8, etc. of A141468 are filled in once at consecutive positions marked N, and a second time at the positions marked P.

Crossrefs

Cf. A000040, A001477, A141468.

Extensions

Entries checked by R. J. Mathar, Aug 06 2009

A167516 Index of A141468(n) in the isolated nonprimes A014574 or the non-isolated nonprimes A164276.

Original entry on oeis.org

1, 2, 1, 2, 3, 4, 5, 3, 6, 7, 8, 4, 9, 10, 11, 12, 13, 14, 15, 16, 5, 17, 18, 19, 20, 21, 22, 23, 24, 6, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 7, 38, 39, 40, 41, 42, 43, 44, 45, 8, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Nov 05 2009

Keywords

Comments

A014574 U A164276 = A141468.

Crossrefs

Cf. A014574, A141468, A164276.

Formula

A014574(a(n)-1)=n or A164276(a(n))=n.

Extensions

Corrected definition and formula index - R. J. Mathar, May 30 2010

A170816 a(n)=A140475(n)-A141468(n).

Original entry on oeis.org

1, 4, 3, 5, 5, 8, 9, 11, 15, 16, 21, 23, 23, 26, 31, 35, 36, 41, 44, 45, 49, 51, 56, 63, 66, 67, 69, 70, 73, 85, 87, 92, 93, 101, 102, 107, 112, 115, 119, 124, 125, 134, 135, 137, 137, 148, 159, 162, 163, 165, 170, 171, 179, 183, 188, 193, 194, 199, 201, 202, 211, 223
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Dec 07 2009

Keywords

Examples

			a(1)=1-0=1, a(2)=5-1=4, a(3)=7-4=3, a(4)=11-6=5, a(5)=13-8=5, a(6)=17-9=8.

Crossrefs

Cf. A140475, A141468.

A173905 {2,3} and the nonprimes A141468.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Mar 02 2010

Keywords

Comments

Essentially the same as A002808, A141468, A018252, A065090, A171581 and A056653.

Crossrefs

Cf. A141468.

Extensions

Replaced the 4-fold negation in the definition by a simpler phrase - R. J. Mathar, Mar 05 2010

A176393 a(n) = A176100(n) + 1 = 2*A141468(n) + 1.

Original entry on oeis.org

1, 3, 9, 13, 17, 19, 21, 25, 29, 31, 33, 37, 41, 43, 45, 49, 51, 53, 55, 57, 61, 65, 67, 69, 71, 73, 77, 79, 81, 85, 89, 91, 93, 97, 99, 101, 103, 105, 109, 111, 113, 115, 117, 121, 125, 127, 129, 131, 133, 137, 139, 141, 145, 149, 151, 153, 155, 157, 161, 163, 165
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Apr 16 2010

Keywords

Programs

  • Maple
    From R. J. Mathar, Apr 20 2010: (Start)
isA001358 := proc(n) numtheory[bigomega](n) = 2 ; end proc:
A176100 :=proc(n) if n = 1 then 0; else for a from procname(n-1)+2 by 2 do if not isA001358(a) then return a; end if; end do: end if; end proc:
A176363 := proc(n) 1+A176100(n) ; end proc: seq(A176363(n),n=1..80) ; (End)

Extensions

Corrected (139 inserted) by R. J. Mathar, Apr 20 2010
Previous Showing 31-40 of 203 results. Next

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

Content is available under The OEIS End-User License Agreement.