A092044 -id:A092044 - cp's OEIS frontend

A105290 Numbers k such that prime(k+1) == 4 (mod k).

1, 3, 11, 13, 69, 71, 637225, 637253, 637313, 637327, 4124459, 4124685, 27067033, 179993017, 179993023, 1208198853, 8179002097, 8179002109, 55762149091

Offset: 1

Zak Seidov, Apr 25 2005

Integers k such that A004649(k+1) = 4. - Michel Marcus, Dec 30 2022

Cf. A023144, A092044.

Cf. A004649, A105286, A105287, A105288, A105329, A105451.

my(n=0, p=2); while(n++, (-4+p=nextprime(p+1))%n || print1(n, ", ")) \\ M. F. Hasler, Feb 05 2009

Missing first two terms inserted by M. F. Hasler, Feb 04 2009
a(11)-a(13) from M. F. Hasler, Feb 05 2009
a(14)-a(15) from Sean A. Irvine, Nov 25 2010
a(16) from D. S. McNeil, Nov 25 2010
a(17)-a(19) from Charles R Greathouse IV, May 05 2011

A156149 Primes p such that prime(p)+2 = 0 (mod p), where prime(p)=A000040(p) is the p-th prime.

Original entry on oeis.org

11, 71, 637319, 637327

Offset: 1

M. F. Hasler, Feb 04 2009

The subsequence of primes in A092044.

Cf. A156154.

p=c=0; until(0, until( isprime(c++), p=nextprime(p+1)); (p+2)%c & next; print1( c","))

a(n) = A000720(A156150(n)) = A000040(A156148(n))

A156151 Primes p such that p+2 = 0 (mod pi(p)), where pi(p)=A000720(p) is the prime counting function.

Original entry on oeis.org

2, 31, 353, 9559783, 9559843, 9559903, 3779853313, 27788573801, 204475054073, 204475054723, 1505578024807, 1505578025779, 241849345578351691, 1784546064357413809, 1784546064357419959, 97199410027249994623, 97199410027250046643, 97199410027250047453, 97199410027250123143

Offset: 1

M. F. Hasler, Feb 04 2009

nonn

Cf. A156152.

p=c=0; until(0, (2+p=nextprime(p+1))%c++ || print1(p",")) \\ PARI syntax for || updated Feb 20 2020

a(n) = A000040(A092044(n)).

More terms from Max Alekseyev, May 03 2009

a(13)-a(19) from Giovanni Resta, Feb 23 2020

A260989 Integers n such that prime(n-1) + prime(n+1) is a multiple of n.

Original entry on oeis.org

4, 5, 8, 11, 12, 18, 20, 70, 72, 1053, 4116, 6459, 6460, 40083, 63328, 251742, 399924, 637320, 637322, 637330, 2582288, 2582436, 2582488, 10553828, 16899042, 69709721, 179992913, 179992922, 465769813, 749973302, 749973314, 1208198617, 1208198629

Offset: 1

Zak Seidov, Aug 06 2015

nonn

			n=4: prime(n-1) + prime(n+1) = 5 + 11 = 16 = 4*n,
n=20: 67 + 73 = 140 = 7*n,
n=16899042: 312632263 + 312632291 = 625264554 = 37*n,
n=69709721: 1394194387 + 1394194453 = 2788388840 = 40*n.

Zak Seidov, Table of n, (c=prime(n-1)+prime(n-1), c/n

Cf. A000040, A004648, A048448, A045924, A023143, A092044, A092045, A156149.

[n: n in [2..7*10^3], k in [2..7*10^3] | (NthPrime(n-1) + NthPrime(n+1)) eq n*k]; // Vincenzo Librandi, Aug 07 2015

Select[Range[2, 100000], Mod[Prime[# - 1] + Prime[# + 1], #] == 0 &] (* Michael De Vlieger, Aug 07 2015 *)

a=2;b=5;for(n=2,10^8,c=a+b;if(c%n<1,print1(n", "));a=nextprime(a+1);b=nextprime(b+1))

p=2;q=3;n=1; forprime(r=5,1e9, if((p+r)%n++==0, print1(n", "));p=q;q=r) \\ Charles R Greathouse IV, Aug 10 2015

a(27)-a(33) from Charles R Greathouse IV, Aug 10 2015

A379014 Least number k such that prime(n) + prime(k) is a multiple of n, or -1 if no such number exists.

Original entry on oeis.org

1, 2, 4, 3, 8, 3, 5, 3, 6, 5, 1, 5, 5, 6, 6, 5, 14, 5, 15, 10, 5, 11, 26, 4, 2, 2, 3, 3, 4, 4, 17, 10, 18, 11, 18, 10, 34, 27, 19, 19, 19, 10, 19, 20, 21, 11, 20, 7, 19, 20, 21, 21, 111, 8, 21, 7, 21, 8, 65, 8, 23, 7, 20, 21, 68, 6, 20, 2, 19, 20, 1, 21, 20, 20

Offset: 1

Jean-Marc Rebert, Dec 13 2024

nonn

Indices n where a(n)=1 correspond with terms of A092044. - Bill McEachen, Dec 21 2024

Cf. A000040, A000720, A068901, A294639.

a[n_]:=Module[{k=1},While[!Divisible[Prime[n]+Prime[k],n], k++]; k]; Array[a,74] (* Stefano Spezia, Dec 13 2024 *)

a(n) = my(k=1, p=prime(n)); while ((p+prime(k)) % n, k++); k; \\ Michel Marcus, Dec 13 2024

a(n) = A000720(A294639(n)). - Pontus von Brömssen, Dec 13 2024

cp's OEIS Frontend

A105290 Numbers k such that prime(k+1) == 4 (mod k).

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A156149 Primes p such that prime(p)+2 = 0 (mod p), where prime(p)=A000040(p) is the p-th prime.

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A156151 Primes p such that p+2 = 0 (mod pi(p)), where pi(p)=A000720(p) is the prime counting function.

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A260989 Integers n such that prime(n-1) + prime(n+1) is a multiple of n.

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A379014 Least number k such that prime(n) + prime(k) is a multiple of n, or -1 if no such number exists.

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