A349660 -id:A349660 - cp's OEIS frontend

A352837 Primes p such that, if q is the next prime, p + q^2 is a prime times a power of 10.

2, 409, 709, 1249, 3229, 4621, 6709, 7069, 7129, 7489, 8209, 9241, 9661, 10789, 11149, 13381, 13789, 15349, 17509, 20641, 21169, 21961, 23509, 25819, 26449, 28309, 28729, 32029, 32089, 34849, 35089, 35809, 37321, 37369, 39769, 40129, 42169, 42349, 42709, 42901, 42979, 44179, 46489, 47269, 47809

Offset: 1

J. M. Bergot and Robert Israel, Apr 05 2022

nonn

Primes prime(k) such that when any trailing zeros are removed from A349660(k), the result is prime.

			a(3) = 709 is a term because 709 and 719 are consecutive primes, 709 + 719^2 = 517670, and 51767 is prime.

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

Cf. A349660, A352848.

R:= NULL: count:= 0:
q:= 2:
while count < 100 do
  p:= q; q:= nextprime(p);
  v:= p+q^2;
  if v mod 10 = 0 then v:= v/10^min(padic:-ordp(v,2),padic:-ordp(v,5)) fi;
  if isprime(v) then count:= count+1; R:= R,p; fi;
od:
R;

f[n_] := n/10^IntegerExponent[n, 10]; Select[Range[50000], PrimeQ[#] && PrimeQ[f[# + NextPrime[#]^2]] &] (* Amiram Eldar, Apr 07 2022 *)

A352851 a(n) = prime(n)^2 + prime(n+1).

Original entry on oeis.org

7, 14, 32, 60, 134, 186, 308, 384, 558, 872, 998, 1410, 1724, 1896, 2262, 2868, 3542, 3788, 4560, 5114, 5408, 6324, 6978, 8018, 9510, 10304, 10716, 11558, 11994, 12896, 16260, 17298, 18908, 19470, 22352, 22958, 24812, 26736, 28062, 30108, 32222, 32952, 36674, 37446, 39008, 39812, 44744, 49956

Offset: 1

Robert Israel, Apr 05 2022

nonn

			a(3) = 5^2 + 7 = 32.

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

Cf. A000040, A001248, A140511, A349660.

seq(ithprime(i)^2+ithprime(i+1), i=1..100);

a[n_] := Prime[n]^2 + Prime[n + 1]; Array[a, 50] (* Amiram Eldar, Apr 07 2022 *)

a(n) = A001248(n) + A000040(n+1).

a(n) = 2*A140511(n), for n>1. - Michel Marcus, Mar 25 2023

A352126 Primes p such that, if q is the next prime, both p+q^2 and p^2+q are primes times powers of 10.

Original entry on oeis.org

2, 4806589, 8369989, 11168569, 20666869, 25068349, 25465249, 29046469, 37597849, 40593349, 44242669, 45405889, 47975869, 49637149, 50057569, 51468349, 57060469, 59570449, 64602589, 64707889, 65940769, 70752049, 75879169, 81799789, 87845869, 90277249, 92415649, 93315889, 95458249, 97225069

Offset: 1

J. M. Bergot and Robert Israel, Apr 05 2022

nonn

Primes prime(k) such that when any trailing zeros are removed from A349660(k) and A352851(k), the results are prime.

Except for 2, each term and the next prime == 19 (mod 30).

			a(3) = 8369989 is a term because it is prime, the next prime is 8370049,
8369989+8370049^2 = 70057728632390, 8369989^2+8370049 = 70056724230170, and 7005772863239 and 7005672423017 are prime.

Robert Israel, Table of n, a(n) for n = 1..250

Cf. A349660, A352851.

Intersection of A352837 and A352852.

R:= NULL: count:= 0:
q:= 2:
while count < 30 do
  p:= q; q:= nextprime(p);
  w:= p+q^2;
  m:= padic:-ordp(w,2);
  if padic:-ordp(w,5) <> m then next fi;
  if m > 0 then w:= w/10^m fi;
  if not isprime(w) then next fi;
  v:= p^2+q;
  m:= padic:-ordp(v,2);
  if padic:-ordp(v,5) <> m then next fi;
  if m > 0 then v:= v/10^m fi;
  if isprime(v) then count:= count+1; R:= R, p; fi
od:
R;

cp's OEIS Frontend

A352837 Primes p such that, if q is the next prime, p + q^2 is a prime times a power of 10.

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A352851 a(n) = prime(n)^2 + prime(n+1).

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A352126 Primes p such that, if q is the next prime, both p+q^2 and p^2+q are primes times powers of 10.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple