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.

A089529 A089528 indexed by A000040.

Original entry on oeis.org

6, 12, 24, 59, 77, 78, 87, 88, 126, 135, 158, 312, 331, 379, 415, 445, 455, 456, 824, 924, 955, 971, 1069, 1080, 1148, 1226, 1368, 1402, 1480, 1592, 1597, 1826, 1934, 2002, 2014, 2035, 2093, 2187, 2212, 2254, 2315, 2353, 2461, 2587, 2619, 2653, 2766, 2792
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			prime(3)=5, 2*5 + 3 = 13 = prime(6);
prime(4)=7, 2*7 + 3 = 17 = prime(7).

Crossrefs

Subsequence of A089532.
Cf. A089526, A089527, A089528.

Formula

a(n) = k such that A089528(n) = A000040(k).
a(n) = A000720(A089528(n)). - Michel Marcus, Aug 04 2021

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 04 2021

A089526 Numbers n such that 2*p(n)+3 and 2*p(n+1)+3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

3, 7, 14, 33, 44, 45, 48, 49, 70, 75, 90, 174, 186, 213, 225, 246, 253, 254, 447, 505, 524, 531, 589, 592, 625, 665, 745, 766, 806, 866, 868, 989, 1047, 1084, 1091, 1105, 1131, 1191, 1202, 1228, 1257, 1280, 1333, 1395, 1410, 1429, 1495, 1512, 1550, 1643, 1651
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			p(3)=5, 2*5+3=13=p(6)
p(4)=7, 2*7+3=17=p(7)

Links

Crossrefs

Subsequence of A089530. Cf. A089527, A089528, A089529.

Programs

  • Mathematica
    cpQ[n_]:=Module[{p=2Prime[n]+3},PrimeQ[p]&&NextPrime[p]==2Prime[n+1]+3]; Select[Range[1700],cpQ] (* Harvey P. Dale, Nov 29 2014 *)

A089450 Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3 are consecutive primes, where p(i) denotes the i-th prime. Sequence terms are 2*p(k) + 3.

Original entry on oeis.org

389, 449, 3217, 31469, 79757, 127297, 130817, 136417, 145349, 168601, 179957, 193577, 198277, 205069, 207377, 231677, 255617, 287137, 300749, 384001, 409589, 515737, 648437, 689917, 750509, 824069, 854869, 982301, 1103437, 1190237
Offset: 1

Views

Author

Ray Chandler, Nov 03 2003

Keywords

Examples

			p(44)=193, 2*193 + 3 = 389 = p(77);
p(45)=197, 2*197 + 3 = 397 = p(78);
p(46)=199, 2*199 + 3 = 401 = p(79).

Crossrefs

Subsequence of A089528.
Cf. A088066, A088119, A089525.

Programs

  • Mathematica
    cpQ[n_]:=Module[{p1=2n+3,p2=2NextPrime[n]+3,p3=2NextPrime[n,2]+3,pr = PrimePi[ 2n+3]},{p1,p2,p3}==Prime[Range[pr,pr+2]]]; 2#+3&/@ Select[ Prime[ Range[50000]],cpQ] (* Harvey P. Dale, Sep 24 2019 *)

Formula

a(n) = 2*A088119(n) + 3 = 2*A000040(A088066(n)) + 3 = A000040(A089525(n)).

Extensions

Definition clarified by Harvey P. Dale, Sep 24 2019
Offset changed to 1 by Jinyuan Wang, Aug 04 2021

A089527 p(k) such that 2*p(k)+3 and 2*p(k+1) + 3 are consecutive primes, where p(i) denotes the i-th prime.

Original entry on oeis.org

5, 17, 43, 137, 193, 197, 223, 227, 349, 379, 463, 1033, 1109, 1303, 1427, 1559, 1607, 1609, 3163, 3613, 3767, 3823, 4289, 4337, 4637, 4969, 5657, 5839, 6199, 6709, 6733, 7823, 8363, 8699, 8747, 8863, 9127, 9643, 9743, 9967, 10253, 10459, 10979, 11593
Offset: 1

Views

Author

Ray Chandler, Nov 07 2003

Keywords

Examples

			p(3)=5, 2*5 + 3 = 13 = p(6);
p(4)=7, 2*7 + 3 = 17 = p(7).

Crossrefs

Subsequence of A023204.
Cf. A089526, A089528, A089529.

Formula

a(n) = A000040(A089526(n)).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 04 2021
Showing 1-4 of 4 results.

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

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