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 1-10 of 18 results. Next

A045958 Numbers k in A045954 such that k+1 is prime.

Original entry on oeis.org

2, 4, 6, 10, 12, 18, 22, 36, 42, 52, 58, 70, 100, 102, 108, 130, 138, 148, 150, 172, 178, 196, 198, 228, 262, 268, 282, 310, 346, 358, 372, 388, 418, 420, 438, 442, 490, 498, 502, 522, 546, 570, 586, 598, 630, 642, 646, 660, 690, 708, 738, 742, 772, 822, 826, 838, 852
Offset: 1

Views

Author

Felice Russo

Keywords

Links

Crossrefs

Cf. A045954, A045959.
Subsequence of A006093.

Programs

  • Mathematica
    seq[max_] := Module[{lst = Range[2, max, 2], i = 2, len}, While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; Select[lst, PrimeQ[# + 1] &]]; seq[1000] (* Amiram Eldar, Mar 20 2024, after Robert G. Wilson v at A045954 *)

Extensions

Title corrected by Sean A. Irvine, Mar 29 2021

A045959 Numbers k in A045954 such that k-1 is prime.

Original entry on oeis.org

4, 6, 12, 18, 20, 42, 44, 54, 68, 84, 90, 98, 102, 108, 114, 132, 138, 140, 150, 164, 182, 198, 212, 228, 230, 234, 278, 282, 308, 314, 332, 354, 374, 390, 420, 434, 458, 522, 524, 548, 570, 578, 588, 602, 614, 642, 644, 660, 674, 684, 710, 740, 822, 882, 884, 938, 954
Offset: 1

Views

Author

Felice Russo

Keywords

Links

Crossrefs

Cf. A045954, A045958.
Subsequence of A008864.

Programs

  • Mathematica
    seq[max_] := Module[{lst = Range[2, max, 2], i = 2, len}, While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; Select[lst, PrimeQ[# - 1] &]]; seq[1000] (* Amiram Eldar, Mar 20 2024, after Robert G. Wilson v at A045954 *)

Extensions

Title corrected by Sean A. Irvine, Mar 29 2021

A045962 Numbers k in A045954 such that 2*k+1 is prime.

Original entry on oeis.org

2, 6, 18, 20, 26, 36, 44, 50, 54, 68, 90, 98, 114, 116, 138, 140, 186, 198, 228, 230, 260, 278, 300, 308, 326, 354, 386, 426, 438, 470, 498, 516, 524, 534, 546, 548, 596, 614, 644, 660, 690, 714, 716, 740, 746, 804, 818, 870, 900, 938, 966, 986, 996, 998, 1044, 1068
Offset: 1

Views

Author

Felice Russo

Keywords

Links

Crossrefs

Cf. A045954, A045963.
Subsequence of A005097.

Programs

  • Mathematica
    seq[max_] := Module[{lst = Range[2, max, 2], i = 2, len}, While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; Select[lst, PrimeQ[2*# + 1] &]]; seq[1000] (* Amiram Eldar, Mar 20 2024, after Robert G. Wilson v at A045954 *)

Extensions

More terms from David W. Wilson
Title corrected by Sean A. Irvine, Mar 29 2021

A045963 Numbers k in A045954 such that 2*k-1 is prime.

Original entry on oeis.org

2, 4, 6, 10, 12, 22, 34, 36, 42, 52, 54, 70, 76, 84, 90, 100, 114, 132, 234, 244, 246, 262, 282, 300, 310, 324, 346, 372, 394, 406, 420, 442, 474, 516, 532, 546, 586, 630, 642, 646, 660, 684, 714, 724, 742, 772, 780, 790, 804, 874, 906, 916, 954, 966, 994, 1002, 1044
Offset: 1

Views

Author

Felice Russo

Keywords

Links

Crossrefs

Cf. A045954, A045962.
Subsequence of A006254.

Programs

  • Mathematica
    seq[max_] := Module[{lst = Range[2, max, 2], i = 2, len}, While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; Select[lst, PrimeQ[2*# - 1] &]]; seq[1000] (* Amiram Eldar, Mar 20 2024, after Robert G. Wilson v at A045954 *)

Extensions

More terms from David W. Wilson
Title corrected by Sean A. Irvine, Mar 29 2021

A045961 Twin A045954's (middle terms) that are primes.

Original entry on oeis.org

3, 5, 11, 19, 43, 53, 101, 131, 139, 149, 197, 229, 373, 389, 419, 523, 547, 587, 643, 709, 739, 883, 997, 1091, 1093, 1187, 1483, 1621, 1931, 1973, 2099, 2243, 2347, 2357, 2411, 2549, 2677, 2731, 2741, 2803, 2963, 3011, 3203, 3307, 3331, 3461, 3467, 3541, 3733
Offset: 1

Views

Author

Felice Russo

Keywords

Comments

Also, prime terms of A045957. - Sean A. Irvine, Mar 29 2021

Links

Crossrefs

Intersection of A000040 and A045957.
Cf. A045954.

Programs

  • Mathematica
    evenLuckies[max_] := Module[{lst = Range[2, max, 2], i = 2, len}, While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; lst]; twinMid[max_] := Module[{s = evenLuckies[max]}, Select[s[[Position[ Differences[s], 2] // Flatten]] + 1, PrimeQ]]; twinMid[3800] (* Amiram Eldar, Mar 20 2024, after Robert G. Wilson v at A045954 *)

Extensions

More terms from David W. Wilson

A045964 Partial sums of A045954.

Original entry on oeis.org

2, 6, 12, 22, 34, 52, 72, 94, 120, 154, 190, 232, 276, 326, 378, 432, 490, 558, 628, 704, 788, 878, 976, 1076, 1178, 1286, 1400, 1516, 1634, 1764, 1896, 2034, 2174, 2322, 2472, 2636, 2806, 2978, 3156, 3338, 3524, 3720, 3918, 4130, 4344, 4562, 4790, 5020, 5254
Offset: 1

Views

Author

Felice Russo

Keywords

Links

Crossrefs

Cf. A045954.

Programs

  • Mathematica
    seq[max_] := Module[{lst = Range[2, max, 2], i = 2, len}, While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; Accumulate[lst]]; seq[250] (* Amiram Eldar, Mar 20 2024, after Robert G. Wilson v at A045954 *)

Extensions

More terms from David W. Wilson

A045989 a(n) = A045954(n)/2.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 10, 11, 13, 17, 18, 21, 22, 25, 26, 27, 29, 34, 35, 38, 42, 45, 49, 50, 51, 54, 57, 58, 59, 65, 66, 69, 70, 74, 75, 82, 85, 86, 89, 91, 93, 98, 99, 106, 107, 109, 114, 115, 117, 122, 123, 130, 131, 134, 139, 141, 145, 149
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A045954.

Programs

  • Mathematica
    seq[max_] := Module[{lst = Range[2, max, 2], i = 2, len}, While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; lst/2]; seq[300] (* Amiram Eldar, Mar 20 2024, after Robert G. Wilson v at A045954 *)

A057747 Number of decompositions of 2n-1 into sum of a lucky number and an even-lucky-number (from A045954).

Original entry on oeis.org

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

Views

Author

Naohiro Nomoto, Oct 30 2000

Keywords

Examples

			1 is not the sum of a lucky number and an even-lucky-number, so a(1)=0; 3=1+2 (one way, so a(2)=1); 5=3+2=1+4 (so a(3)=2); etc.

Links

Crossrefs

Cf. A000959, A045954.

Extensions

Offset changed to 1 by Jinyuan Wang, Apr 07 2020

A118125 Difference between the even Lucky numbers (A045954) minus the odd Lucky numbers (A000959).

Original entry on oeis.org

-1, -1, 1, -1, 1, -3, 1, 3, 5, -1, 1, 1, 5, 1, 11, 13, 11, 5, 5, 3, 3, 3, 1, 5, 9, 7, 13, 13, 15, 5, 9, 13, 19, 15, 19, 7, 19, 21, 17, 19, 19, 15, 21, 11, 17, 17, 9, 11, 25, 17, 21, 13, 21, 17, 11, 15, 13, 9, 19, 13, 17, 17, 15, 23, 25, 15, 13, 27, 29, 21, 25, 23, 27, 31, 33, 23, 15, 31, 37, 41
Offset: 1

Views

Author

Robert G. Wilson v, May 11 2006

Keywords

Crossrefs

Cf. A000959, A045954.

Programs

  • Mathematica
    ev = Range[2, 435, 2]; i = 2; While[ i <= (len = Length@ev) && (k = ev[[i]]) <= len, ev = Drop[ev, {k, len, k}]; i++ ]; od = Range[1, 476, 2]; i = 2; While[ i <= (len = Length@od) && (k = od[[i]]) <= len, od = Drop[od, {k, len, k}]; i++ ]; od - ev

Formula

a(n) = A045954(n) - A000959(n).

A194282 Variant of the even lucky numbers (A045954).

Original entry on oeis.org

2, 6, 10, 14, 18, 26, 30, 34, 38, 50, 54, 58, 62, 74, 78, 82, 86, 102, 106, 110, 114, 122, 126, 130, 134, 154, 158, 162, 170, 178, 182, 194, 202, 210, 222, 226, 230, 246, 250, 254, 258, 266, 270, 274, 278, 290, 298, 314, 318, 326, 338, 342, 346, 354, 370
Offset: 1

Views

Author

Alonso del Arte, Aug 22 2011

Keywords

Comments

Write down even numbers: 2, 4, 6, 8, ...; first term is 2 so starting from 2 remove every second number: 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, ...; next number is 6 so remove every 6th term starting from 2: 2, 6, 10, 14, 18, 26, 30, 34, 38, 42, 50, ...; etc.
This differs from the even lucky numbers in that for those the first step of removals consists of removing every fourth number rather than every second number as is done here. Michon calls this starting "the sieving directly with p = 2."

Links

Programs

  • Mathematica
    lst = Range[2, 320, 2]; i = 1; While[i <= (len = Length@lst) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++]; lst (* Alonso del Arte, based on Robert G. Wilson v's program for A045954, Aug 22 2011 *)
Showing 1-10 of 18 results. Next

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

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