cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A107019 Records in A074928.

Original entry on oeis.org

1, 2, 6, 8, 14, 24, 30, 32, 58, 60, 68, 70, 84, 102
Offset: 1

Views

Author

Zak Seidov, May 10 2005

Keywords

Crossrefs

Cf. A107057: Positions of records in A074928.

A107057 Positions of records in A074928.

Original entry on oeis.org

1, 2, 5, 7, 13, 26, 67, 88, 114, 405, 446, 554, 598, 784
Offset: 1

Views

Author

Zak Seidov, May 10 2005

Keywords

Crossrefs

Cf. A107019: Records in A074928.

A107058 a(n) = smallest number m>0 such that prime(n)*prime(n+1)-m is a prime.

Original entry on oeis.org

1, 2, 4, 4, 4, 10, 6, 4, 6, 12, 18, 6, 4, 4, 14, 6, 6, 8, 6, 4, 18, 4, 18, 4, 6, 4, 18, 6, 16, 4, 4, 8, 6, 4, 16, 18, 2, 10, 12, 18, 18, 22, 6, 10, 4, 6, 2, 22, 6, 4, 6, 6, 34, 8, 2, 18, 6, 26, 24, 30, 6, 12, 6, 16, 30, 10, 8, 6, 22, 6, 8, 4, 2, 8, 18, 26, 10, 4, 12, 30, 10, 12, 4, 24, 6, 6, 6
Offset: 1

Views

Author

Zak Seidov, May 10 2005

Keywords

Comments

a(n) is even for n > 1. - Seiichi Manyama, Mar 17 2025

Crossrefs

Cf. A107059: records in A107058; A106172: positions of records in A107058. Cf. A074928: a(n)>0 such that p(n)*p(n+1)+a(n) is a smallest prime.

Programs

  • PARI
    a(n) = { my(m=0, v = prime(n)*prime(n+1)); while (! isprime(v-m), m++;); return (m);} \\ Michel Marcus, Apr 19 2013

A106172 Positions of records in A107058.

Original entry on oeis.org

1, 2, 3, 6, 10, 11, 42, 53, 89, 142, 204, 238, 324, 434, 764, 926
Offset: 1

Views

Author

Zak Seidov, May 10 2005

Keywords

Crossrefs

A107059 Records in A107058.

Original entry on oeis.org

1, 2, 4, 10, 12, 18, 22, 34, 36, 40, 48, 50, 76, 84, 86, 112
Offset: 1

Views

Author

Zak Seidov, May 10 2005

Keywords

Crossrefs

Cf. A106172: positions of records in A107058.

A120941 a(n)=k-n where prime(k) is the smallest prime greater than prime(n)*prime(n+1).

Original entry on oeis.org

3, 5, 9, 18, 30, 42, 60, 77, 113, 145, 179, 229, 262, 293, 353, 430, 487, 545, 622, 671, 737, 826, 916, 1052, 1184, 1249, 1310, 1373, 1443, 1654, 1894, 2026, 2131, 2298, 2481, 2602, 2782, 2943, 3107, 3298, 3436, 3651, 3866, 3975, 4083, 4346, 4808, 5144
Offset: 1

Views

Author

Axel Harvey, Aug 18 2006

Keywords

Comments

Parity of A120941: 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, ....

Examples

			The product of the 4th prime number, 7 and the 5th prime, 11, is 77; the smallest prime greater than this is the 22nd prime, 79; therefore the 4th term of the sequence is 22-4 = 18.
		

Crossrefs

Programs

  • Maple
    f:= n -> numtheory:-pi(ithprime(n)*ithprime(n+1))+1-n:
    map(f, [$1..100]); # Robert Israel, Mar 21 2017
  • Mathematica
    Table[PrimePi[Prime[n]Prime[n + 1]] - n + 1, {n, 48}] (* Zak Seidov, Aug 21 2006 *)
  • PARI
    for(n=1, 100, print1(primepi(prime(n)*prime(n + 1)) - n + 1, ", ")) \\ Indranil Ghosh, Mar 22 2017
    
  • Python
    from sympy import prime, primepi
    print([primepi(prime(n)*prime(n + 1)) - n + 1 for n in range(1, 100)]) # Indranil Ghosh, Mar 22 2017

Formula

a(n) = A000720(A006094(n)) + 1 - n. - Robert Israel, Mar 21 2017

Extensions

More terms from Robert G. Wilson v, Aug 21 2006

A105692 Minimal a(n)>0, not appeared previously, such that p(n)*p(n+1)+a(n) is prime.

Original entry on oeis.org

1, 2, 6, 12, 8, 18, 14, 20, 10, 30, 4, 26, 24, 32, 40, 36, 38, 42, 44, 48, 16, 50, 46, 56, 54, 60, 62, 68, 74, 72, 66, 34, 78, 96, 114, 82, 52, 108, 58, 84, 80, 102, 110, 92, 90, 28, 70, 86, 98, 122, 76, 120, 116, 94, 88, 22, 138, 100, 132, 104, 128, 156, 126, 158, 146, 144
Offset: 1

Views

Author

Zak Seidov, Apr 17 2005

Keywords

Comments

1 and permutation(?) of even integers. Cf. A074928

Crossrefs

Cf. A074928.
Showing 1-7 of 7 results.