A253969 -id:A253969 - cp's OEIS frontend

A253970 Primes p such that p + nextprime(p) is divisible by 5.

2, 13, 29, 43, 47, 59, 103, 113, 149, 157, 163, 167, 179, 193, 199, 223, 239, 257, 269, 293, 313, 367, 401, 419, 463, 491, 509, 557, 569, 587, 599, 607, 613, 619, 643, 647, 659, 673, 677, 701, 727, 761, 773, 809, 823, 853, 863, 883, 911, 947, 953, 977, 1019

Offset: 1

Vincenzo Librandi, Jan 23 2015

Primes p such that p + nextprime(p) is divisible by 10 is the same as this sequence without the term 2. - Derek Orr, Jan 30 2015

			p=29 is in this sequence because 29+31 = 60 is divisible by 5.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A253969.

[p: p in PrimesUpTo(1500) | (p+NextPrime(p)) mod 5 eq 0];

Prime@Select[Range[300], Mod[Prime[#] + Prime[# + 1], 5]==0 &]
Transpose[Select[Partition[Prime[Range[200]],2,1],Divisible[Total[ #],5]&]] [[1]] (* Harvey P. Dale, Feb 10 2015 *)

forprime(p=1,10^3,if(!((p+nextprime(p+1))%5),print1(p,", "))) \\ Derek Orr, Jan 30 2015

A253972 Primes p such that p + nextprime(p) is divisible by 8.

Original entry on oeis.org

3, 11, 53, 59, 61, 71, 73, 107, 113, 139, 157, 173, 179, 191, 227, 233, 239, 257, 283, 293, 311, 317, 347, 353, 373, 419, 431, 433, 523, 541, 547, 557, 593, 599, 601, 631, 653, 659, 677, 691, 733, 773, 787, 811, 827, 919, 941, 953, 977, 1013, 1019, 1031, 1033

Offset: 1

Vincenzo Librandi, Jan 23 2015

			p=59 is in this sequence because 59+61 = 120 is divisible by 8.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A253969.

[p: p in PrimesUpTo(1500) | (p+NextPrime(p)) mod 8 eq 0];

Prime@Select[Range[300], Mod[Prime[#] + Prime[# + 1], 8]==0 &]
Select[Partition[Prime[Range[200]],2,1],Mod[Total[#],8]==0&][[;;,1]] (* Harvey P. Dale, Aug 28 2024 *)

forprime(p=1,10^3,if(!((p+nextprime(p+1))%8),print1(p,", "))) \\ Derek Orr, Jan 30 2015

A253973 Primes p such that p + nextprime(p) is divisible by 9.

Original entry on oeis.org

7, 17, 43, 71, 79, 97, 107, 139, 179, 197, 223, 269, 277, 283, 313, 317, 337, 349, 401, 409, 431, 439, 457, 491, 521, 673, 743, 761, 787, 809, 827, 839, 853, 881, 907, 1021, 1039, 1061, 1087, 1151, 1193, 1213, 1277, 1303, 1373, 1399, 1429, 1447, 1471, 1483

Offset: 1

Vincenzo Librandi, Jan 28 2015

			p=43 is in this sequence because 43+47 = 90 is divisible by 9.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. similar sequences listed in A253969.

[p: p in PrimesUpTo(1500) | (p+NextPrime(p)) mod 9 eq 0];

Prime@Select[Range[300], Mod[Prime[#] + Prime[# + 1], 9]==0 &]
Select[Partition[Prime[Range[300]],2,1],Divisible[Total[#],9]&][[All,1]] (* Harvey P. Dale, Jul 27 2017 *)

forprime(p=1,10^3,if(!((p+nextprime(p+1))%9),print1(p,", "))) \\ Derek Orr, Jan 30 2015

A348578 Primes that begin a record list of consecutive primes whose sum of any 2 consecutive terms is divisible by 3.

Original entry on oeis.org

5, 89, 809, 3954889, 15186319, 77011289, 288413159, 62585146739, 114058236679, 143014298809, 2320700383121, 2942277160583, 4386778243843, 16104860854333, 23171469790747

Offset: 1

Michel Marcus, Oct 24 2021

The Rivera link gives the first 15 terms.

			A001043 begins as (5, 8, 12, 18, 24, 30, 36, 42, 52) where 7 consecutive terms are multiple of 3 starting at 3rd term, corresponding to 5=prime(3), so 5 is the 1st term of this sequence.

Carlos Rivera, Puzzle 1059 Set of consecutive primes such that..., The Prime Puzzles and Problems Connection.

Cf. A001043, A253969.

p=2;t=r=0;Monitor[Do[p=NextPrime[p];t=0;While[Mod[p+NextPrime@p,3]==0,p=NextPrime@p;t++];If[t>r,Print[NextPrime[p,-t]];r=t],{n,10^14}],p] (* Giorgos Kalogeropoulos, Oct 24 2021 *)

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A253970 Primes p such that p + nextprime(p) is divisible by 5.

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A253972 Primes p such that p + nextprime(p) is divisible by 8.

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Magma

Mathematica

PARI

A253973 Primes p such that p + nextprime(p) is divisible by 9.

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Author

Keywords

Examples

Links

Crossrefs

Programs

Magma

Mathematica

PARI

A348578 Primes that begin a record list of consecutive primes whose sum of any 2 consecutive terms is divisible by 3.

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Keywords

Comments

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Programs

Mathematica