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.

A171871 Triangle read by rows: Distinct classifications of N elements containing exactly R binary partitions.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 3, 3, 0, 0, 0, 3, 17, 6, 0, 0, 0, 1, 36, 74, 11, 0, 0, 0, 1, 60, 573, 358, 23, 0, 0, 0, 0, 56, 2802, 7311, 1631, 47, 0, 0, 0, 0, 50, 10087, 107938, 83170, 7563, 106, 0, 0, 0, 0, 27, 26512, 1186969, 3121840, 866657, 34751, 235, 0, 0, 0, 0, 19
Offset: 0

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Author

Robert Munafo, Jan 21 2010

Keywords

Comments

Significance of triangle suggested by Franklin T. Adams-Watters on Dec 19 2009. Row N has N terms in this sequence. The triangle starts:
1;
0, 1;
0, 0, 1;
0, 0, 1, 2;
0, 0, 0, 3, 3;
0, 0, 0, 0, 3, 17, 6;
0, 0, 0, 0, 1, 36, 74, 11;
Value is A000055(N) when R=N-1 (last term in each row). (Conjectured by Robert Munafo Dec 28 2009, then proved by Andrew Weimholt and Franklin T. Adams-Watters on Dec 29 2009)
Value is 1 when N=2^R.
Value is 1 when N=(2^R)-1.
Value is R when R>2 and N=(2^R)-2.
Value is A034198(R) when R>2 and N=(2^R)-3.
Conjecture: In general, in each column, the last 2^(R-1) values are the same as the first 2^(N-1) values from the corresponding row of A039754. - Robert Munafo, Dec 30 2009
Value is 0 for all (N,R) for which N is greater than 2^R.
Each term A(N,R) can be computed most efficiently by first enumerating all classifications in A(N-1,R) plus those in A(N-1,R-1), and then adding an additional type and/or partition to each.

Links

Crossrefs

Cf. Row sums are A005646, column sums are A171832.
Cf. A039754.
Last term in each row is A000055(N).
Same triangle read by columns is A171872.

A271666 Primes p such that 4*p^2+4*p-1 is prime.

Original entry on oeis.org

2, 3, 7, 13, 17, 23, 31, 37, 53, 59, 67, 139, 149, 151, 157, 167, 179, 193, 199, 223, 233, 293, 307, 331, 359, 373, 389, 431, 479, 571, 587, 619, 643, 653, 683, 809, 839, 857, 863, 919, 937, 947, 1021, 1091, 1123, 1151, 1187, 1277, 1301, 1367, 1427, 1511
Offset: 1

Views

Author

Vincenzo Librandi, Apr 12 2016

Keywords

Links

Crossrefs

Cf. A171139, A171831, A171832, A261810.

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | IsPrime(4*p^2+4*p-1)];
  • Mathematica
    Select[Prime[Range[300]], PrimeQ[4 #^2 + 4 # - 1] &]
  • PARI
    lista(nn) = forprime(p=2, nn, if(isprime(4*p^2+4*p-1), print1(p, ", "))); \\ Altug Alkan, Apr 12 2016
  • Python
    from gmpy2 import is_prime
for p in range(3,10**5,2):
    if(not is_prime(p)):continue
    elif(is_prime(6*p**2+6*p-1)):print(p)
# Soumil Mandal, Apr 14 2016

A271667 Primes p such that 6*p^2+6*p-1 is prime.

Original entry on oeis.org

3, 5, 13, 41, 43, 61, 71, 73, 103, 113, 181, 223, 241, 269, 271, 283, 379, 433, 479, 491, 521, 523, 593, 619, 631, 659, 719, 839, 929, 941, 1009, 1039, 1069, 1193, 1249, 1289, 1319, 1429, 1433, 1471, 1489, 1511, 1553, 1601, 1613, 1693, 1699, 1723, 1753, 1861
Offset: 1

Views

Author

Vincenzo Librandi, Apr 12 2016

Keywords

Examples

			3 is a term because 3 is prime and 6*3^2+6*3-1 is 71 which is prime. 13 is a term because 13 is prime and 6*13^2+6*13-1 is 1091 which is prime. - _Soumil Mandal_, Apr 14 2016

Links

Crossrefs

Cf. A171139, A171831, A171832, A261810, A271666.

Programs

  • Magma
    [p: p in PrimesUpTo(2000) | IsPrime(6*p^2+6*p-1)];
  • Mathematica
    Select[Prime[Range[300]], PrimeQ[6 #^2 + 6 # - 1] &]
  • PARI
    lista(nn) = forprime(p=2, nn, if(isprime(6*p^2+6*p-1), print1(p, ", "))); \\ Altug Alkan, Apr 12 2016
  • Python
    from gmpy2 import is_prime
for p in range(3,10**5,2):
    if(not is_prime(p)):continue
    elif(is_prime(6*p**2+6*p-1)):print(p)
# Soumil Mandal, Apr 14 2016
Showing 1-3 of 3 results.

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