A017293 -id:A017293 - cp's OEIS frontend

A017298 a(n) = (10*n + 2)^6.

64, 2985984, 113379904, 1073741824, 5489031744, 19770609664, 56800235584, 139314069504, 304006671424, 606355001344, 1126162419264, 1973822685184, 3297303959104, 5289852801024, 8198418170944

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

Cf. A001014 (n^6), A017293 (10n+2).

[(10*n+2)^6: n in [0..25]]; // Vincenzo Librandi, Jul 30 2011

(10*Range[0,20]+2)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{64,2985984,113379904,1073741824,5489031744,19770609664,56800235584},20] (* Harvey P. Dale, Aug 12 2012 *)

for n in range(0, 25): print((10*n + 2)**6, end=", ") # Stefano Spezia, Oct 20 2018

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(0)=64, a(1)=2985984, a(2)=113379904, a(3)=1073741824, a(4)=5489031744, a(5)=19770609664, a(6)=56800235584. - Harvey P. Dale, Aug 12 2012

A031919 a(n) = prime(10*n-8).

Original entry on oeis.org

3, 37, 79, 131, 181, 239, 293, 359, 421, 479, 557, 613, 673, 743, 821, 881, 953, 1021, 1091, 1163, 1231, 1301, 1399, 1459, 1531, 1601, 1667, 1747, 1831, 1907, 1997, 2069, 2137, 2237, 2297, 2377, 2441, 2543, 2633, 2693, 2753, 2837, 2917

Offset: 1

Jeff Burch

nonn

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Cf. A000040, A017293.

[ &+[(NthPrime(10*n-8))]: n in [1..1000] ]; // Vincenzo Librandi, Apr 08 2011

a(n) = prime(10*n-8); \\ Michel Marcus, May 04 2020

a(n) = A000040(A017293(n-1)). - Michel Marcus, May 04 2020

A154405 Primes of the form 20n^2+8n+1.

Original entry on oeis.org

29, 97, 353, 541, 769, 1693, 2081, 4621, 8161, 9857, 13729, 14797, 17053, 19469, 24781, 26209, 32321, 35617, 42689, 48413, 54497, 65437, 72481, 77377, 85021, 87649, 95773, 98561, 125453, 141793, 148609, 152077, 166349, 177473, 185089

Offset: 1

Vincenzo Librandi, Jan 09 2009

			For n=1, a(1)=29; n=2, a(2)=97

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A017293

[a: n in [0..200] | IsPrime(a) where a is 20*n^2+8*n+1];

Select[Table[20n^2+8n+1,{n,0,600}],PrimeQ]

12701 removed, 32321 inserted, 18609 replaced by 148609 - R. J. Mathar, Feb 19 2009

Misleading formula removed - R. J. Mathar, Oct 18 2010

A277987 a(n) = 100*n - 28.

Original entry on oeis.org

-28, 72, 172, 272, 372, 472, 572, 672, 772, 872, 972, 1072, 1172, 1272, 1372, 1472, 1572, 1672, 1772, 1872, 1972, 2072, 2172, 2272, 2372, 2472, 2572, 2672, 2772, 2872, 2972, 3072, 3172, 3272, 3372, 3472, 3572, 3672, 3772, 3872, 3972

Offset: 0

Emeric Deutsch, Nov 12 2016

For n>=1, a(n) is the second Zagreb index of the tetrameric 1,3-adamantane TA[n]. The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph. The pictorial definition of the tetrameric 1,3-adamantane can be viewed in the G. H. Fath-Tabar et al. reference.

The M-polynomial of the tetrameric 1,3-adamantane TA[n] is M(TA[n],x,y) = 6*(n+1)*x^2*y^3 + 6*(n-1)*x^2*y^4 + (n-1)*x^4*y^4.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
G. H. Fath-Tabar, A. Azad, and N. Elahinezhad, Some topological indices of tetrameric 1,3-adamantane, Iranian J. Math. Chemistry, 1, No. 1, 2010, 111-118.
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A277986.

[100*n-28: n in [0..40]]; // Vincenzo Librandi, Nov 13 2016

Maple
```
seq(100*n-28, n = 0..40);
```

100*Range[0,40]-28 (* or *) LinearRecurrence[{2,-1},{-28,72},50] (* Harvey P. Dale, Feb 13 2018 *)

a(n) = 100*n - 28 \\ Felix Fröhlich, Nov 12 2016

G.f.: 4*(32*x - 7)/(1 - x)^2.
a(n) = A017293(10*n-3) for n > 0. - Felix Fröhlich, Nov 12 2016
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Nov 13 2016

A346651 a(n) is the number of divisors of A139245(n) ending with 2.

Original entry on oeis.org

1, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 2, 4, 2, 2, 3, 2, 3, 4, 2, 2, 3, 2, 3, 5, 2, 3, 3, 2, 2, 4, 3, 2, 3, 4, 2, 4, 2, 3, 3, 2, 2, 5, 3, 2, 6, 2, 2, 4, 2, 3, 3, 3, 2, 4, 2, 4, 3, 3, 3, 5, 2, 2, 3, 2, 2, 7, 4, 2, 4, 2, 2, 4, 3, 3, 3, 2, 3, 6, 2, 3, 3, 4, 2, 4, 2, 2, 5, 2

Offset: 1

Stefano Spezia, Jul 26 2021

a(n) is odd if and only if A139245(n) either is the square of a number ending with 2 or has a unitary prime divisor ending with 7.

The term 1 appears only for n = 1 in corresponding to A139245(1) = 4.

			a(14) = 4 since there are 4 divisors of A139245(14) = 264 ending with 2: 2, 12, 22 and 132.

Cf. A000005, A017293 (numbers ending with 2), A017294 (squares of numbers ending with 2), A030432, A056169, A139245 (product of two numbers ending with 2), A346388, A346389.

a[n_]:=Length[Drop[Select[Divisors[20n-16], (Last[IntegerDigits[#]]==2&)]]]; Array[a, 90]

a(n) = sumdiv(20*n-16, d, (d%10) == 2); \\ Michel Marcus, Jul 26 2021

A384735 Numbers that are prime or end in a prime number (of any length).

Original entry on oeis.org

2, 3, 5, 7, 11, 12, 13, 15, 17, 19, 22, 23, 25, 27, 29, 31, 32, 33, 35, 37, 41, 42, 43, 45, 47, 52, 53, 55, 57, 59, 61, 62, 63, 65, 67, 71, 72, 73, 75, 77, 79, 82, 83, 85, 87, 89, 92, 93, 95, 97, 101, 102, 103, 105, 107, 109, 111, 112, 113, 115, 117

Offset: 1

Mohd Anwar Jamal Faiz, Jun 08 2025

If k is a term, so is m*10^A055642(k) + k for all m > 0. - Michael S. Branicky, Jun 10 2025

			2, 3, 5, 7 and 11 are terms since they are prime.
15 is a term since it ends in the prime 5.
111 is a term since it ends in the prime 11.

Mohd Anwar Jamal Faiz, Primender Sequence: A Novel Mathematical Construct for Testing Symbolic Inference and AI Reasoning, arXiv:2506.10585 [cs.AI], 2025. See pp. 4, 9.

Cf. A000040, A033664, A055642.

Contains A017293, A017305, A017329, A017353.

q:= n-> isprime(n) or (k-> k>1 and q(n mod 10^(k-1)))(length(n)):
select(q, [$1..150])[];  # Alois P. Heinz, Jun 08 2025

q[n_] := AnyTrue[Range[1, IntegerLength[n]-1], PrimeQ[Mod[n, 10^#]] &]; Select[Range[120], PrimeQ[#] || q[#] &] (* Amiram Eldar, Jun 10 2025 *)

isok(x) = my(y=x, nb=0); while(y>1, y/=10; nb++; if (isprime(x%(10^nb)), return(1))); \\ Michel Marcus, Jun 10 2025

from sympy import isprime
def ok(n):
    s = str(n)
    return any(isprime(int(s[i:])) for i in range(len(s)))
print([k for k in range(118) if ok(k)])

cp's OEIS Frontend

A017298 a(n) = (10*n + 2)^6.

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A031919 a(n) = prime(10*n-8).

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A154405 Primes of the form 20n^2+8n+1.

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A277987 a(n) = 100*n - 28.

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A346651 a(n) is the number of divisors of A139245(n) ending with 2.

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A384735 Numbers that are prime or end in a prime number (of any length).

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Maple

Mathematica

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Python