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.

A077278 Duplicate of A073683.

Original entry on oeis.org

2, 5, 13, 31, 43, 67, 79, 97, 131, 179, 199, 257, 293, 313, 359, 389, 409, 431, 443, 467
Offset: 1

Views

Author

Keywords

A073684 Sum of next a(n) successive primes is prime.

Original entry on oeis.org

2, 3, 5, 3, 5, 3, 3, 7, 9, 5, 9, 7, 3, 7, 5, 3, 3, 3, 5, 3, 3, 3, 5, 5, 57, 25, 49, 3, 9, 5, 11, 3, 5, 5, 5, 5, 17, 25, 3, 3, 5, 3, 7, 9, 5, 3, 3, 3, 15, 3, 3, 3, 3, 3, 3, 3, 15, 3, 5, 33, 5, 3, 3, 9, 7, 3, 33, 3, 3, 5, 3, 15, 3, 5, 9, 7, 13, 5, 11, 3, 3, 11
Offset: 1

Views

Author

Amarnath Murthy, Aug 11 2002

Keywords

Comments

Group the primes such that the sum of each group is a prime. Each group from the second onwards should contain at least 3 primes: (2, 3), (5, 7, 11), (13, 17, 19, 23, 29), (31, 37, 41), (43, 47, 53, 59, 61), ... Sequence gives number of terms in each group.

Examples

			a(1)=2 because sum of first two primes 2+3 is prime; a(2)=3 because sum of next three primes 5+7+11 is prime; a(3)=5 because sum of next five primes 13+17+19+23+29 is prime.

Links

Crossrefs

Cf. A073682(n) is the sum of terms in n-th group, A073683(n) is the first term in n-th group, A077279(n) is the last term in n-th group.

Programs

  • Mathematica
    f[l_List] := Block[{n = Length[Flatten[l]], k = 3, r},While[r = Table[Prime[i], {i, n + 1, n + k}]; ! PrimeQ[Plus @@r], k += 2];Append[l, r]];Length /@ Nest[f, {{2, 3}}, 100] (* Ray Chandler, May 11 2007 *)
cnt = 0; Table[s = Prime[cnt+1] + Prime[cnt+2]; len = 2; While[! PrimeQ[s], len++; s = s + Prime[cnt+len]]; cnt = cnt + len; len, {n, 100}] (* T. D. Noe, Feb 06 2012 *)
  • Python
    from itertools import count, islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    s, i, p = 0, 1, 2
    while True:
        while not(isprime(s:=s+p)) or i < 2:
            i, p = i+1, nextprime(p)
        yield i
        s, i, p = 0, 1, nextprime(p)
print(list(islice(agen(), 82))) # Michael S. Branicky, May 23 2025

Extensions

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 10 2003
Extended by Ray Chandler, May 02 2007

A073682 Prime sum of n-th group of successive primes in A073684.

Original entry on oeis.org

5, 23, 101, 109, 263, 211, 251, 757, 1367, 941, 2053, 1901, 911, 2347, 1861, 1187, 1249, 1303, 2273, 1433, 1493, 1553, 2777, 2927, 44843, 26699, 65713, 4597, 14159, 8069, 18439, 5197, 8819, 9011, 9277, 9419, 33599, 53381, 6761, 6823, 11497, 7013
Offset: 1

Views

Author

Amarnath Murthy, Aug 11 2002

Keywords

Comments

Partition the sequence of primes into groups so that the sum of the terms in each group is prime: {2, 3}, {5, 7, 11}, {13, 17, 19, 23, 29}, {31, 37, 41}, {43, 47, 53, 59, 61}, {67, 71, 73}, {79, 83, 89}, {97, 101, 103, 107, 109, 113, 127}, {131, 137, 139, 149, 151, 157, 163, 167, 173}, {179, 181, 191, 193, 197}, ...; A073684(n) is the number of terms in n-th group; A073682(n) is the sum of terms in n-th group; A073683(n) is the first term in n-th group; A077279(n) is the last term in n-th group.

Examples

			a(1)=5 because sum of first two primes 2+3 = 5 is prime;
a(2)=23 because sum of next three primes 5+7+11 = 23 is prime;
a(3)=101 because sum of next five primes 13+17+19+23+29 = 101 is prime.

Links

Crossrefs

Cf. A073683, A073684, A077279.

Programs

  • Python
    from itertools import count, islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    s, i, p = 0, 1, 2
    while True:
        while not(isprime(s:=s+p)) or i < 2:
            i, p = i+1, nextprime(p)
        yield s
        s, i, p = 0, 1, nextprime(p)
print(list(islice(agen(), 42))) # Michael S. Branicky, May 23 2025

Extensions

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 10 2003

A077279 Last prime of n-th group of successive primes in A073684.

Original entry on oeis.org

3, 11, 29, 41, 61, 73, 89, 127, 173, 197, 251, 283, 311, 353, 383, 401, 421, 439, 463, 487, 503, 523, 569, 599, 983, 1153, 1511, 1543, 1601, 1621, 1721, 1741, 1783, 1823, 1871, 1901, 2029, 2239, 2267, 2281, 2311, 2341, 2383, 2447, 2503, 2539, 2551, 2591
Offset: 1

Views

Author

Zak Seidov, Nov 02 2002

Keywords

Comments

Partition the sequence of primes into groups so that the sum of the terms in each group is prime: {2, 3}, {5, 7, 11}, {13, 17, 19, 23, 29}, {31, 37, 41}, {43, 47, 53, 59, 61}, {67, 71, 73}, {79, 83, 89}, {97, 101, 103, 107, 109, 113, 127}, {131, 137, 139, 149, 151, 157, 163, 167, 173}, {179, 181, 191, 193, 197},..; A073684(n) is the number of terms in n-th group; A073682(n) is the sum of terms in n-th group; A073683(n) is the first term in n-th group; A077279(n) is the last term in n-th group.

Crossrefs

Cf. A073684, A092285, A073683.

Programs

  • Python
    from itertools import count, islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    s, i, p = 0, 1, 2
    while True:
        while not(isprime(s:=s+p)) or i < 2:
            i, p = i+1, nextprime(p)
        yield p
        s, i, p = 0, 1, nextprime(p)
print(list(islice(agen(), 48))) # Michael S. Branicky, May 23 2025
Showing 1-4 of 4 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.