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 1-3 of 3 results.

A102725 Smallest prime equal to the sum of n distinct pairs of consecutive primes.

Original entry on oeis.org

5, 13, 31, 43, 67, 97, 139, 191, 227, 311, 373, 433, 523, 607, 719, 827, 947, 1091, 1229, 1367, 1511, 1663, 1861, 2039, 2237, 2423, 2633, 2861, 3089, 3329, 3617, 3877, 4133, 4421, 4721, 5009, 5351, 5659, 6011, 6359, 6761, 7121, 7517, 7877, 8273, 8663, 9137
Offset: 1

Views

Author

Giovanni Teofilatto, Feb 07 2005

Keywords

Examples

			a(1) = 5 = (2+3).
a(2) = 13 = (2+3)+(3+5).
a(3) = 31 = (2+3)+(3+5)+(7+11).

Crossrefs

Cf. A001043, A102724, A102729.

Extensions

Edited and extended by Ray Chandler, Feb 12 2005

A102729 Triangle read by rows: n-th row consists of lexicographically least set of n distinct terms of A001043 whose sum is minimal prime.

Original entry on oeis.org

5, 5, 8, 5, 8, 18, 5, 8, 12, 18, 5, 8, 12, 18, 24, 5, 8, 12, 18, 24, 30, 5, 8, 12, 18, 24, 30, 42, 5, 8, 12, 18, 24, 30, 42, 52, 5, 8, 12, 18, 24, 30, 36, 42, 52, 5, 8, 12, 18, 24, 30, 36, 42, 52, 84, 5, 8, 12, 18, 24, 30, 36, 42, 52, 68, 78, 5, 8, 12, 18, 24, 30, 36, 42, 52, 60, 68, 78
Offset: 1

Views

Author

Giovanni Teofilatto, Feb 07 2005

Keywords

Comments

A001043 gives sums of consecutive primes.

Examples

			5
5,8
5,8,18
5,8,12,18
5,8,12,18,24

Crossrefs

Cf. A001043, A102724; A102725 gives row sum.

Extensions

Edited and extended by Ray Chandler, Feb 12 2005

A378569 a(n) = 3*n*(n+1) + 7.

Original entry on oeis.org

7, 13, 25, 43, 67, 97, 133, 175, 223, 277, 337, 403, 475, 553, 637, 727, 823, 925, 1033, 1147, 1267, 1393, 1525, 1663, 1807, 1957, 2113, 2275, 2443, 2617, 2797, 2983, 3175, 3373, 3577, 3787, 4003, 4225, 4453, 4687, 4927, 5173, 5425, 5683, 5947, 6217, 6493, 6775, 7063, 7357, 7657, 7963, 8275, 8593, 8917, 9247, 9583, 9925
Offset: 0

Views

Author

M. F. Hasler, Feb 04 2025

Keywords

Comments

The terms a(1) = 13 through a(7) = 175, coincide with A102724(2..8), cumulative sums of pairs of primes. From a(8) = 223, it differs from A102724(9) = 227.

Links

Crossrefs

Cf. A001043, A102724.

Programs

Formula

a(n) = A102724(n+1) for 1 <= n <= 7, where A102724 = partial sums of A001043(n) = prime(n)+prime(n+1).
From Vincenzo Librandi, Feb 06 2025: (Start)
a(n) = 2* a(n-1) - a(n-2) + 6.
G.f.: (7-8x+7x^2)/ (1-3x+3x^2-x^3). (End)
E.g.f.: exp(x)*(7 + 6*x + 3*x^2). - Stefano Spezia, Feb 06 2025
Showing 1-3 of 3 results.

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

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