A017221 -id:A017221 - cp's OEIS frontend

A301623 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 5.

23, 41, 59, 77, 113, 131, 149, 167, 203, 221, 239, 257, 293, 311, 329, 347, 383, 401, 419, 437, 473, 491, 509, 527, 563, 581, 599, 617, 653, 671, 689, 707, 743, 761, 779, 797, 833, 851, 869, 887, 923, 941, 959, 977, 1013, 1031, 1049, 1067, 1103, 1121

Offset: 1

Gary Croft, Mar 24 2018

Numbers == {23, 41, 59, 77} mod 90 with additive sum sequence 23{+18+18+18+36} {repeat ...}. Includes all primes number > 5 with digital root 5.

			23+18=41; 41+18=59; 59+18=77; 77+36=113; 113+18=131.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Intersection of A007775 and A017221.

Filtered(Filtered([1..1200],n->n mod 2 <> 0 and n mod 3 <> 0 and n mod 5 <> 0),i->i-9*Int((i-1)/9)=5); # Muniru A Asiru, Apr 22 2018

LinearRecurrence[{1,0,0,1,-1},{23,41,59,77,113},50] (* Harvey P. Dale, Jul 28 2018 *)

Vec(x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 25 2018

Numbers == {23, 41, 59, 77} mod 90.
From Colin Barker, Mar 25 2018: (Start)
G.f.: x*(23 + 18*x + 18*x^2 + 18*x^3 + 13*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
(End)

A367856 Table T(n,k), read by downward antidiagonals: T(n,k) = floor((3T(n,k-1)+2)/2) starting with T(n,0) = 3n.

Original entry on oeis.org

0, 1, 3, 2, 5, 6, 4, 8, 10, 9, 7, 13, 16, 14, 12, 11, 20, 25, 22, 19, 15, 17, 31, 38, 34, 29, 23, 18, 26, 47, 58, 52, 44, 35, 28, 21, 40, 71, 88, 79, 67, 53, 43, 32, 24, 61, 107, 133, 119, 101, 80, 65, 49, 37, 27, 92, 161, 200, 179, 152, 121, 98, 74, 56, 41, 30

Offset: 0

Philippe Deléham, Dec 03 2023

Permutation of nonnegative numbers.

			Square array starts:
  0,  1,  2,  4,   7,  11,  17,  26,  40,   61, ...
  3,  5,  8, 13,  20,  31,  47,  71, 107,  161, ...
  6, 10, 16, 25,  38,  58,  88, 133, 200,  301, ...
  9, 14, 22, 34,  52,  79, 119, 179, 269,  404, ...
 12, 19, 29, 44,  67, 101, 152, 229, 344,  517, ...
 15, 23, 35, 53,  80, 121, 182, 274, 412,  619, ...
 18, 28, 43, 65,  98, 148, 223, 335, 503,  755, ...
 21, 32, 49, 74, 112, 169, 254, 382, 574,  862, ...
 24, 37, 56, 85, 128, 193, 290, 436, 655,  983, ...
 27, 41, 62, 94, 142, 214, 322, 484, 727, 1091, ...
 ...

Paolo Xausa, Table of n, a(n) for n = 0..11324 (first 150 antidiagonals, flattened).
Index entries for sequences that are permutations of the natural numbers.

Cf. A001651, A006999, A008585, A017173, A017221.

A367856[n_, k_] := A367856[n, k] = If[k == 0, 3*n, Floor[3*A367856[n, k-1]/2 + 1]];
Table[A367856[k, n-k], {n, 0, 10}, {k, 0, n}] (* Paolo Xausa, Apr 03 2024 *)

T(n,0) = 3*n = A008585(n).
T(2*n,1) = 9*n+1 = A017173(n).
T(2*n+1,1) = 9*n+5 = A017221(n).
T(0,k) = A006999(k).
T(2^k+n, k) = 3^(k+1) + T(n, k).

More terms from Paolo Xausa, Apr 03 2024

A031904 a(n) = prime(9*n - 4).

Original entry on oeis.org

11, 43, 83, 131, 179, 229, 277, 337, 389, 443, 499, 569, 617, 673, 739, 809, 859, 929, 991, 1049, 1103, 1181, 1237, 1301, 1381, 1451, 1499, 1571, 1621, 1699, 1777, 1861, 1913, 1997, 2063, 2129, 2207, 2273, 2341, 2393, 2467, 2551, 2647

Offset: 1

Jeff Burch

nonn

Cf. A017221.

[ NthPrime(9*n-4): n in [1..50] ]; // Vincenzo Librandi, Apr 09 2011

Prime[9 Range[50]-4] (* Harvey P. Dale, Mar 15 2023 *)

A309844 Primes of the form n^4 + n^2 + 3.

Original entry on oeis.org

3, 5, 23, 653, 10103, 83813, 160403, 234743, 280373, 1049603, 3420653, 6252503, 11319863, 52207853, 92246423, 146422103, 174913853, 221548343, 442071653, 479807123, 577224653, 607597853, 655385603, 937921253, 1222865933, 1249233683, 1387525253, 1506177293

Offset: 1

Christopher R. Madan, Aug 19 2019

Digital root of all values > 3 is 5, compare A017221.

Subset of A027753. Subset of A017221.

Cf. A037896, A182344, A182345, A049423.

a = [];
for n = 0:1e3
    x = n.^4+n.^2+3;
    if isprime(x); a = [a,x]; end;
end

f[n_] := n^4 + n^2 + 3; Select[f /@ Range[0, 200], PrimeQ] (* Amiram Eldar, Aug 24 2019 *)

from sympy import isprime
a = []
for n in range(0,1000):
    x = n**4+n**2+3
    if isprime(x):
        a.append(x)

cp's OEIS Frontend

A301623 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 5.

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A367856 Table T(n,k), read by downward antidiagonals: T(n,k) = floor((3*T(n,k-1)+2)/2) starting with T(n,0) = 3*n.

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A031904 a(n) = prime(9*n - 4).

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A309844 Primes of the form n^4 + n^2 + 3.

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A367856 Table T(n,k), read by downward antidiagonals: T(n,k) = floor((3T(n,k-1)+2)/2) starting with T(n,0) = 3n.