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 1-4 of 4 results.

A268497 Records in A268630 (= a(n)^2+a(n+1) is prime).

Original entry on oeis.org

0, 2, 4, 8, 10, 16, 18, 23, 28, 32, 37, 48, 63, 66, 73, 76, 79, 82, 99, 100, 102, 106, 109, 126, 142, 147, 169, 172, 177, 178, 189, 190, 198, 201, 205, 208, 217, 225, 226, 228, 232, 235, 244, 253, 258, 264, 268, 278, 288, 306, 333, 336, 343, 348, 352, 358, 361, 370, 379, 382
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2016

Keywords

Comments

See A268496 for the corresponding indices, A268494-A268495 for "late birds". We use offset 0 here because the first term has a special status (it's not really "late") and also because all related sequences (A268630 and A268494 - A268497) have a(0)=0 and omitting this term yields the corresponding "positive integer" variant.

Programs

  • PARI
    show(n, f="/tmp/b268497.txt", c=0, a=0, u=[a-1])={for(n=1, n, a>=u[#u]&&if(f, write(f, c++-1, " "a), print1(a", ")); u=setunion(u, [a]); while(#u>1&&u[2]==u[1]+1, u=u[^1]); for(k=u[1]+1, 9e9, !setsearch(u, k) && isprime(a*a+k) && (a=k) && break))}

A268494 Indices n of "late birds" (a(n)n) in A268630 (= a(n)^2+a(n+1) is prime).

Original entry on oeis.org

0, 2, 4, 12, 13, 14, 21, 44, 69, 76, 107, 109, 114, 127, 204, 214, 246, 249, 298, 317, 394, 402, 420, 440, 442, 477, 504, 508, 533, 550, 552, 610, 632, 647, 656, 682, 743, 745, 801, 808, 925, 943, 952, 954, 961, 966, 980, 1010, 1050, 1089, 1112, 1162, 1167, 1200, 1229, 1233, 1244, 1389, 1401, 1415, 1423, 1432, 1462
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2016

Keywords

Comments

See A268495 for the corresponding values. We use offset 0 here because the first term has a special status (it's not really "late") and also because all related sequences (A268630 and A268494 - A268497) have a(0)=0 and omitting this term yields the corresponding "positive integer" variant.
Assuming that A268630 is a permutation of the nonnegative integers N (as conjectured), the characterization given in the name is equivalent to say that a(n) equals the least number not occurring earlier. The sequence defined that way is finite if and only if A268630 is not a permutation of N.

Links

Programs

  • PARI
    show(n,a=0,u=[a-1])={for(n=1, n, a==u[1]+1&&print1(n-1","); u=setunion(u,[a]); while(#u>1&&u[2]==u[1]+1,u=u[^1]); for(k=u[1]+1, 9e9, !setsearch(u, k) && isprime(a*a+k) && (a=k) && break))}

A268495 "Late birds" (a(n)n) in A268630 (= a(n)^2+a(n+1) is prime).

Original entry on oeis.org

0, 1, 3, 5, 6, 11, 14, 17, 26, 61, 62, 74, 77, 80, 101, 179, 191, 206, 209, 212, 269, 329, 341, 383, 401, 404, 425, 455, 458, 461, 467, 491, 557, 560, 581, 605, 614, 668, 680, 731, 734, 824, 869, 875, 890, 893, 911, 923, 935, 944, 959, 1031, 1064, 1097, 1118, 1130, 1151, 1154, 1316, 1322, 1328, 1349
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2016

Keywords

Comments

See A268494 for the corresponding indices, A268496-A268497 for records. We use offset 0 here because the first term has a special status (it's not really "late") and also because all related sequences (A268630 and A268494 - A268497) have a(0)=0 and omitting this term yields the corresponding "positive integer" variant.
Assuming that A268630 is a permutation of the nonnegative integers N (as conjectured), the characterization given in the name is equivalent to say that a(n) equals the least number not occurring earlier. The sequence defined that way is finite if and only if A268630 is not a permutation of N.

Links

Programs

  • PARI
    show(n,f="/tmp/b268495.txt",c=0,a=0,u=[a-1])={for(n=1, n, a==u[1]+1&&if(f,write(f,c++-1," "a),print1(a",")); u=setunion(u,[a]); while(#u>1&&u[2]==u[1]+1,u=u[^1]); for(k=u[1]+1, 9e9, !setsearch(u, k) && isprime(a*a+k) && (a=k) && break))}

A268496 Indices of records in A268630 (= a(n)^2+a(n+1) is prime).

Original entry on oeis.org

0, 1, 3, 5, 7, 9, 15, 16, 17, 23, 24, 29, 40, 49, 52, 63, 72, 73, 74, 77, 83, 89, 92, 93, 105, 110, 130, 145, 154, 161, 162, 165, 175, 182, 184, 189, 190, 198, 205, 213, 217, 218, 219, 222, 237, 239, 247, 251, 253, 255, 278, 293, 308, 311, 313, 331, 336, 339, 346, 351, 353, 362, 366
Offset: 0

Views

Author

M. F. Hasler, Feb 09 2016

Keywords

Comments

See A268497 for the actual record values.

Programs

  • PARI
    show(n, f="/tmp/b268496.txt", c=0, a=0, u=[a-1])={for(n=1, n, a>=u[#u]&&if(f, write(f, c++-1, " "n-1), print1(n-1", ")); u=setunion(u, [a]); while(#u>1&&u[2]==u[1]+1, u=u[^1]); for(k=u[1]+1, 9e9, !setsearch(u, k) && isprime(a*a+k) && (a=k) && break))}
Showing 1-4 of 4 results.

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

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