A287653 -id:A287653 - cp's OEIS frontend

A340408 Primes p such that pq+qr+r*s is prime, where q,r,s are the next primes after p.

3, 17, 19, 23, 43, 151, 157, 199, 229, 233, 331, 347, 461, 467, 491, 503, 523, 547, 563, 613, 617, 619, 653, 739, 743, 773, 941, 1021, 1031, 1051, 1063, 1097, 1103, 1117, 1163, 1193, 1237, 1259, 1279, 1373, 1429, 1489, 1523, 1553, 1601, 1609, 1613, 1627, 1663, 1709, 1733, 1907, 1999, 2011, 2087

Offset: 1

J. M. Bergot and Robert Israel, Jan 06 2021

nonn

			a(3) = 19 is a term because 19*23+23*29+29*31 = 2003 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A287653.

q:= 2: r:= 3: s:= 5:
count:= 0: R:= NULL:
while count < 100 do
  p:= q; q:= r; r:= s; s:= nextprime(s);
  if isprime(p*q+q*r+r*s) then count:= count+1; R:= R, p;  fi
od:
R;

from sympy import isprime, nextprime
def aupton(terms):
  p, q, r, s, alst = 2, 3, 5, 7, []
  while len(alst) < terms:
    if isprime(p*q + q*r + r*s): alst.append(p)
    p, q, r, s = q, r, s, nextprime(s)
  return alst
print(aupton(55)) # Michael S. Branicky, Mar 17 2021

A340537 Primes that are sums of a sequence of consecutive terms of A006094.

Original entry on oeis.org

127, 491, 1201, 1427, 2003, 2713, 2767, 5431, 7229, 7639, 13001, 17231, 18061, 20753, 24509, 37337, 37589, 38149, 38261, 44563, 44839, 50969, 51517, 53609, 55201, 60859, 76519, 77191, 80239, 80783, 81703, 90823, 91583, 96493, 103079, 103687, 110573, 126713, 130411, 134093, 137777, 139199, 139663

Offset: 1

J. M. Bergot and Robert Israel, Jan 10 2021

nonn

Each term is the sum of at least three consecutive terms of A006094.

A number that can be expressed as such a sum in more than one way is only listed once. The first such number is 50911291 = 547*557+...+1051*1061 = 1423*1427+...+1559*1567.

			a(1) = 5*7+7*11+11*13 = 127.
a(2) = 5*7+7*11+11*13+13*17+17*19 = 491.
a(3) = 11*13+13*17+17*19+19*23+23*29 = 1201.
a(4) = 19*23+23*29+29*31 = 1427.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A006094, A340465. Includes A287653.

SP:= [seq(ithprime(i)*ithprime(i+1),i=1..100)]:
SSP:= ListTools:-PartialSums([0,op(SP)]):
select(t -> t <= SP[-1] and isprime(t),
  {seq(seq(SSP[j]-SSP[i],i=1..j-3),j=4..nops(SSP))});

cp's OEIS Frontend

A340408 Primes p such that pq+qr+r*s is prime, where q,r,s are the next primes after p.

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A340537 Primes that are sums of a sequence of consecutive terms of A006094.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

cp's OEIS Frontend

A340408 Primes p such that p*q+q*r+r*s is prime, where q,r,s are the next primes after p.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Python

A340537 Primes that are sums of a sequence of consecutive terms of A006094.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

A340408 Primes p such that pq+qr+r*s is prime, where q,r,s are the next primes after p.