A260181 Numbers whose last digit is prime.

2, 3, 5, 7, 12, 13, 15, 17, 22, 23, 25, 27, 32, 33, 35, 37, 42, 43, 45, 47, 52, 53, 55, 57, 62, 63, 65, 67, 72, 73, 75, 77, 82, 83, 85, 87, 92, 93, 95, 97, 102, 103, 105, 107, 112, 113, 115, 117, 122, 123, 125, 127, 132, 133, 135, 137, 142, 143, 145, 147

Offset

1,1

Comments

Numbers ending in 2, 3, 5 or 7.

The subsequence of primes is A042993. - Michel Marcus, Jul 19 2015

From Wesley Ivan Hurt, Aug 15 2015, Sep 26 2015: (Start)

Ceiling(a(n)/2) = A047201(n).

Complement of (A197652 Union A262389). (End)

Links

Muniru A Asiru, Table of n, a(n) for n = 1..5000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

G.f.: x*(2+x+2*x^2+2*x^3+3*x^4) / ((x-1)^2*(1+x+x^2+x^3)).

a(n) = a(n-1)+a(n-4)-a(n-5), n>5.

a(n) = (5*n-4-(-1)^n+((3-(-1)^n)/2)*(-1)^((2*n+5-(-1)^n)/4))/2.

Maple

A260181:=n->(5*n-4-(-1)^n+((3-(-1)^n)/2)*(-1)^((2*n+5-(-1)^n)/4))/2: seq(A260181(n), n=1..100);

Mathematica

CoefficientList[Series[(2 + x + 2 x^2 + 2 x^3 + 3 x^4)/((x - 1)^2*(1 + x + x^2 + x^3)), {x, 0, 100}], x]
LinearRecurrence[{1, 0, 0, 1, -1}, {2, 3, 5, 7, 12}, 60] (* Vincenzo Librandi, Jul 18 2015 *)
Table[(5n - 4 - (-1)^n + ((3 - (-1)^n)/2)*(-1)^((2*n + 5 - (-1)^n)/4))/2, {n, 100}] (* Wesley Ivan Hurt, Aug 11 2015 *)

Prog

(Magma) [(5*n-4-(-1)^n+((3-(-1)^n) div 2)*(-1)^((2*n+5-(-1)^n) div 4))/2: n in [1..70]]; // Vincenzo Librandi, Jul 18 2015
(PARI) is(n)=my(m=digits(n)); isprime(m[#m]) \\ Anders Hellström, Jul 19 2015
(PARI) A260181(n)=(n--)\4*10+prime(n%4+1) \\ is(n)=isprime(n%10) is much more efficient than the above. - M. F. Hasler, Sep 16 2016
(GAP) a:=n->(5*n-4-(-1)^n+((3-(-1)^n)/2)*(-1)^((2*n+5-(-1)^n)/4))/2; List([1..60], n->a(n)); # Muniru A Asiru, Feb 16 2018

Crossrefs

Cf. A042993, A047201, A092620, subset of A118950.

Union of A017293, A017305, A017329 and A017353.

First differences are [1,2,2,5,...] = A002522(A140081(n-1)).

Cf. A197652, A262389.

Sequence in context: A092620 A028843 A028842 * A140971 A073689 A257560

Adjacent sequences: A260178 A260179 A260180 * A260182 A260183 A260184

Keyword

nonn,base,easy

Author

Wesley Ivan Hurt, Jul 17 2015

Status

approved