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.

A361485 Primes p such that p + 1024 is also prime.

Original entry on oeis.org

7, 37, 67, 73, 79, 127, 139, 157, 163, 193, 199, 277, 283, 337, 349, 409, 457, 463, 487, 499, 547, 577, 613, 643, 673, 709, 787, 823, 853, 877, 883, 907, 1039, 1063, 1087, 1117, 1129, 1213, 1249, 1327, 1399, 1423, 1453, 1567, 1597, 1609, 1663, 1669, 1753, 1777, 1873, 1879
Offset: 1

Views

Author

Elmo R. Oliveira, Mar 13 2023

Keywords

Comments

All terms are == 1 (mod 6).

Examples

			139 and 139 + 1024 = 1163 are both prime.

Links

Crossrefs

Cf. A000040.
Cf. sequences of the type p + k are primes: A001359 (k = 2), A023200 (k = 4), A023202 (k = 8), A049488 (k = 16), A049489 (k = 32), A049490 (k = 64), A049491 (k = 128), A361483 (k = 256), A361484 (k = 512), this sequence (k = 1024).

Programs

  • PARI
    lista(nn)=my(v=vector(nn), p=2); for(n=1, nn, until(isprime(p+1024), p=nextprime(p+1)); v[n]=p); v \\ Winston de Greef, Mar 20 2023

A054987 Smallest composite x such that sigma(x+2^n) = sigma(x) + 2^n.

Original entry on oeis.org

434, 305635357, 27, 39, 106645, 69, 2275, 63, 6475, 249, 7735, 3703, 10803, 16383, 58869, 51181, 87951, 1695, 9579, 105237, 98829, 1143369, 789609, 11625, 14038691, 178975, 48627929, 1881333, 402373721, 2667945, 82915599, 353195221, 70106601
Offset: 1

Views

Author

Labos Elemer, May 29 2000

Keywords

Comments

The sequence is initiated by smallest of A015915. Special primes of A023202, A049488-A049491 also satisfy the Sigma[p+2^w]=Sigma[p]+2^w relation

Examples

			For the term 69: Sigma[69+2^6] = Sigma[133] = 1+7+19+133 = Sigma[69]+64 = (1+3+23+69)+64 = 160.

Crossrefs

Cf. A049488-A049491, A001359, A054799, A015913, A015915, A023200, A023202, A054905.

Programs

  • Mathematica
    Table[ Select[ Range[ 1, 110000 ], Equal[ EulerPhi[ #+2^k ]-EulerPhi[ # ]-2^k, 0 ] &&!PrimeQ[ # ]& ], {k, 1, 22} ]
  • PARI
    a(n)=my(N=2^n,x=3); while(isprime(x++) || sigma(x+N) != sigma(x)+N,); x \\ Charles R Greathouse IV, Mar 11 2014

Extensions

More terms from Labos Elemer, Aug 14 2003
a(21) corrected and a(27)-a(33) from Donovan Johnson, Nov 30 2008

A361483 Primes p such that p + 256 is also prime.

Original entry on oeis.org

7, 13, 37, 61, 97, 103, 127, 163, 193, 211, 223, 307, 313, 331, 337, 397, 421, 463, 487, 541, 571, 601, 607, 631, 673, 691, 727, 757, 853, 907, 937, 967, 1021, 1033, 1051, 1063, 1117, 1153, 1171, 1231, 1237, 1297, 1303, 1327, 1381, 1453, 1531, 1567, 1621, 1657, 1693, 1723
Offset: 1

Views

Author

Elmo R. Oliveira, Mar 13 2023

Keywords

Comments

All terms are == 1 (mod 6).

Examples

			61 and 61 + 256 = 317 are both prime.

Crossrefs

Cf. A000040.
Cf. sequences of the type p + k are primes: A001359 (k = 2), A023200 (k = 4), A023202 (k = 8), A049488 (k = 16), A049489 (k = 32), A049490 (k = 64), A049491 (k = 128), this sequence (k = 256), A361484 (k = 512), A361485 (k = 1024).

A361484 Primes p such that p + 512 is also prime.

Original entry on oeis.org

11, 29, 59, 89, 101, 107, 131, 149, 179, 197, 227, 239, 257, 311, 317, 347, 479, 509, 521, 557, 617, 641, 659, 701, 719, 809, 887, 911, 941, 947, 971, 977, 1019, 1031, 1097, 1109, 1151, 1181, 1187, 1229, 1277, 1289, 1319, 1361, 1367, 1439, 1481, 1487, 1499, 1571, 1601
Offset: 1

Views

Author

Elmo R. Oliveira, Mar 13 2023

Keywords

Comments

All terms are == 5 (mod 6).

Examples

			59 and 59 + 512 = 571 are both prime.

Crossrefs

Cf. A000040.
Cf. sequences of the type p + k are primes: A001359 (k = 2), A023200 (k = 4), A023202 (k = 8), A049488 (k = 16), A049489 (k = 32), A049490 (k = 64), A049491 (k = 128), A361483 (k = 256), this sequence (k = 512), A361485 (k = 1024).

A361679 A(n,k) is the n-th prime p such that p + 2^k is also prime; square array A(n,k), n>=1, k>=1, read by antidiagonals.

Original entry on oeis.org

3, 3, 5, 3, 7, 11, 3, 5, 13, 17, 5, 7, 11, 19, 29, 3, 11, 13, 23, 37, 41, 3, 7, 29, 31, 29, 43, 59, 7, 11, 19, 41, 37, 53, 67, 71, 11, 13, 23, 37, 47, 43, 59, 79, 101, 7, 29, 37, 29, 43, 71, 67, 71, 97, 107, 5, 37, 59, 61, 53, 67, 107, 73, 89, 103, 137
Offset: 1

Views

Author

Alois P. Heinz, Mar 20 2023

Keywords

Examples

			Square array A(n,k) begins:
    3,   3,   3,   3,   5,   3,   3,   7,  11,   7, ...
    5,   7,   5,   7,  11,   7,  11,  13,  29,  37, ...
   11,  13,  11,  13,  29,  19,  23,  37,  59,  67, ...
   17,  19,  23,  31,  41,  37,  29,  61,  89,  73, ...
   29,  37,  29,  37,  47,  43,  53,  97, 101,  79, ...
   41,  43,  53,  43,  71,  67,  71, 103, 107, 127, ...
   59,  67,  59,  67, 107,  73,  83, 127, 131, 139, ...
   71,  79,  71,  73, 131, 103, 101, 163, 149, 157, ...
  101,  97,  89,  97, 149, 109, 113, 193, 179, 163, ...
  107, 103, 101, 151, 167, 127, 149, 211, 197, 193, ...

Links

Crossrefs

Columns k=1-10 give: A001359, A023200, A023202, A049488, A049489, A049490, A049491, A361483, A361484, A361485.
Row n=1 gives A056206.
Main diagonal gives A361680.
Cf. A000040.

Programs

  • Maple
    A:= proc() option remember; local f; f:= proc() [] end;
      proc(n, k) option remember; local p;
        p:= `if`(nops(f(k))=0, 1, f(k)[-1]);
        while nops(f(k))
Showing 1-5 of 5 results.

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