A290450 -id:A290450 - cp's OEIS frontend

A007652 Final digit of prime(n).

2, 3, 5, 7, 1, 3, 7, 9, 3, 9, 1, 7, 1, 3, 7, 3, 9, 1, 7, 1, 3, 9, 3, 9, 7, 1, 3, 7, 9, 3, 7, 1, 7, 9, 9, 1, 7, 3, 7, 3, 9, 1, 1, 3, 7, 9, 1, 3, 7, 9, 3, 9, 1, 1, 7, 3, 9, 1, 7, 1, 3, 3, 7, 1, 3, 7, 1, 7, 7, 9, 3, 9, 7, 3, 9, 3, 9, 7, 1, 9, 9, 1, 1, 3, 9, 3, 9, 7, 1, 3, 7, 9, 7, 1, 9, 3, 9, 1, 3, 1, 7, 7, 3, 9, 1

Offset: 1

N. J. A. Sloane, Simon Plouffe

Primes modulo 10.

Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 870.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Milton Abramowitz and Irene A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Alberto Fraile et al., Prime numbers and random walks in a square grid, Phys. Rev. E, 104(5) (2021), 054114.
Evelyn Lamb, "Peculiar Pattern Found in 'Random' Prime Numbers", Nature, March 14, 2016, republished by Scientific American.
Robert J. Lemke Oliver and Kannan Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv preprint arXiv:1603.03720 [math.NT], 2016.
Index entries for sequences related to final digits of numbers.

Cf. A000040, A010879, A110923, A039701-A039706, A038194, A039709-A039715, A290450.

[Intseq(p)[1]: p in PrimesUpTo(600)]; // Bruno Berselli, Feb 14 2013

[p mod 10: p in PrimesUpTo(500)]; // Vincenzo Librandi, May 06 2014

seq(ithprime(n) mod 10, n=1..105); # Nathaniel Johnston, Jun 29 2011

Table[Mod[Prime[n], 10], {n, 120}] (* Ray Chandler, Oct 01 2005 *)
Mod[Prime[Range[100]], 10] (* Vincenzo Librandi, May 06 2014 *)

a(n)=prime(n)%10 \\ Charles R Greathouse IV, Oct 13 2016

primes(100)%10 \\ Charles R Greathouse IV, Oct 13 2016

a(n) = A010879(A000040(n)). - Michel Marcus, May 06 2014

Sum_k={1..n} a(k) ~ 5*n. - Amiram Eldar, Dec 11 2024

Extended by Ray Chandler, Oct 01 2005

A031928 Lower prime of a difference of 10 between consecutive primes.

Original entry on oeis.org

139, 181, 241, 283, 337, 409, 421, 547, 577, 631, 691, 709, 787, 811, 829, 919, 1021, 1039, 1051, 1153, 1171, 1249, 1399, 1471, 1627, 1699, 1723, 1801, 1879, 2017, 2029, 2053, 2089, 2143, 2521, 2647, 2719, 2731, 2767, 2887, 2917, 3001, 3109, 3361, 3517, 3547, 3571, 3583, 3709, 3769, 3823, 3853, 4201, 4219, 4231, 4243, 4261, 4273, 4327, 4339, 4363, 4483, 4663, 4861, 4909, 4957, 5011, 5179, 5323, 5581, 5659, 5701, 5791, 5869, 6079, 6091

Offset: 1

Lekraj Beedassy, Jul 23 2003

Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n). Namely, a(n)^(1/n) is a strictly decreasing function of n (see comments at A248855). - Jahangeer Kholdi and Farideh Firoozbakht, Nov 29 2014

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for primes, gaps between

Cf. A023203, A053323, A248855, A290450.

[p: p in PrimesUpTo(7000) | NextPrime(p)-p eq 10]; // Bruno Berselli, Apr 09 2013

Transpose[Select[Partition[Prime[Range[800]], 2, 1], #[[2]] - #[[1]] == 10&]] [[1]] (* Harvey P. Dale, Oct 02 2014 *)
p = Prime@Range@800; p[[Flatten@Position[Differences@p, 10]]] (* Hans Rudolf Widmer, Aug 28 2022 *)

forprime(p=o=1,1e4,10+o==(o=p)&&print1(p-10",")) \\ M. F. Hasler, Mar 10 2017

a(n) = prime(A320703(n)). - R. J. Mathar, Apr 30 2024

Edited by Labos Elemer, Jul 25 2003

A328452 Primes p such that p=prime(k), prime(k+1), and prime(k+2) end in the same digit.

Original entry on oeis.org

1627, 3089, 4297, 4831, 6481, 6793, 8543, 11027, 11867, 13421, 13649, 14177, 17509, 17807, 18839, 18859, 20359, 20411, 22501, 22511, 22963, 22973, 24923, 25189, 26449, 26459, 27367, 27541, 28309, 29443, 29453, 31081, 32203, 32381, 34919, 35171, 35281, 36343, 36353, 37087, 37223, 37243, 38923

Offset: 1

Philip Mizzi, Oct 15 2019

			(p,q,r) = (1627,1637,1657), are three primes which are consecutive and end in the same digit. Hence, p=1627 is a member of this sequence.

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

Cf. A000040, A290450, A054681.

f:=func; a:=[]; for p in PrimesUpTo(40000) do if f(p,1) or f(p,3) or f(p,7) or f(p,9) then Append(~a,p); end if; end for; a; // Marius A. Burtea, Oct 16 2019

q:= 3: r:= 5: count:= 0: R:= NULL:
while count < 100 do
   p:= q; q:= r; r:= nextprime(r);
   if p-q mod 10 = 0 and q-r mod 10 = 0 then count:= count+1; R:= R, p; fi
od:
R; # Robert Israel, May 08 2020

First /@ Select[Partition[Prime@ Range@ 4105, 3, 1], Length@ Union@ Mod[#, 10] == 1 &] (* Giovanni Resta, Oct 16 2019 *)

isok(p) = {if (isprime(p), my(d = p % 10); my(q = nextprime(p+1), r = nextprime(q+1)); (d == (q % 10)) && (d == (r % 10)););} \\ Michel Marcus, Oct 17 2019

A298075 Primes p whose last digit is the same as that of both its predecessor prime and its successor prime.

Original entry on oeis.org

1637, 3109, 4327, 4861, 6491, 6803, 8563, 11047, 11887, 13441, 13669, 14197, 17519, 17827, 18859, 18869, 20369, 20431, 22511, 22531, 22973, 22993, 24943, 25219, 26459, 26479, 27397, 27551, 28319, 29453, 29473, 31091, 32213, 32401, 34939, 35201, 35291, 36353, 36373

Offset: 1

K. D. Bajpai, Jan 11 2018

69623 is the least prime in this sequence that is equidistant from its predecessor prime (69593) and its successor prime (69653).

			1637 is in the sequence because it is prime with last digit 7, and both its predecessor prime (1627) and successor prime (1657) also end in 7.
3109 is in the sequence because each of the three consecutive primes 3089, 3109, and 3119 ends in 9.
3119 is not in the sequence: although it is prime and both it and its predecessor prime (3109) end with the digit 9, the next prime (3121) does not.

Subsequence of A290450.

Select[Partition[Prime[Range[10000]], 3, 1], Mod[#[[1]], 10] == Mod[#[[2]], 10] == Mod[#[[3]], 10] &][[All, 2]]

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A007652 Final digit of prime(n).

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A031928 Lower prime of a difference of 10 between consecutive primes.

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A328452 Primes p such that p=prime(k), prime(k+1), and prime(k+2) end in the same digit.

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Magma

Maple

Mathematica

PARI

A298075 Primes p whose last digit is the same as that of both its predecessor prime and its successor prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica