A072003 -id:A072003 - cp's OEIS frontend

A106727 Triangle T(n,k) = (f(n+1)*f(k+1) mod 10), where f(j) = 10 - (prime(j+3) mod 10), read by rows.

9, 7, 1, 1, 3, 9, 9, 7, 1, 9, 3, 9, 7, 3, 1, 1, 3, 9, 1, 7, 9, 3, 9, 7, 3, 1, 7, 1, 7, 1, 3, 7, 9, 3, 9, 1, 9, 7, 1, 9, 3, 1, 3, 7, 9, 7, 1, 3, 7, 9, 3, 9, 1, 7, 1, 1, 3, 9, 1, 7, 9, 7, 3, 1, 3, 9, 9, 7, 1, 9, 3, 1, 3, 7, 9, 7, 1, 9, 1, 3, 9, 1, 7, 9, 7, 3, 1, 3, 9, 1, 9

Offset: 0

Roger L. Bagula, May 14 2005

			Triangle begins:
  9;
  7, 1;
  1, 3, 9;
  9, 7, 1, 9;
  3, 9, 7, 3, 1;
  1, 3, 9, 1, 7, 9;
  3, 9, 7, 3, 1, 7, 1;

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Cf. A007652, A072003.

f[n_]:= 10 - Mod[Prime[n+3], 10];
Table[Mod[f[n+1]*f[k+1], 10], {n,0,15}, {k,0,n}]//Flatten

def f(n): return 10 - (nth_prime(n+3)%10)
def A106727(n,k): return (f(n+1)*f(k+1))%10
flatten([[A106727(n,k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Sep 10 2021

T(n, k) = (f(n+1)*f(k+1) mod 10) where f(j) = 10 - (prime(j+3) mod 10).

A122754 a(n) = 10*n - A101306(n).

Original entry on oeis.org

8, 15, 20, 23, 32, 39, 42, 43, 50, 51, 60, 63, 72, 79, 82, 89, 90, 99, 102, 111, 118, 119, 126, 127, 130, 139, 146, 149, 150, 157, 160, 169, 172, 173, 174, 183, 186, 193, 196, 203, 204, 213, 222, 229, 232, 233, 242, 249, 252, 253

Offset: 1

Roger L. Bagula, Sep 21 2006

Cf. A101306.

Partial sums of A072003.

Table[Sum[10 - Mod[Prime[n], 10], {n, 1, m}], {m, 1, 50}]

a(n) = Sum_{i=1..n} (10 - A007652(n)).

Definition simplified by the Assoc. Eds. of the OEIS, Mar 27 2010

A071641 a(n) defined by recursion in the formula section.

Original entry on oeis.org

1, 1, 1, 1, 3, 7, 9, 3, 7, 3, 7, 3, 5, 7, 7, 7, 9, 8, 7, 5, 7, 7, 3, 3, 9, 3, 3, 1, 7, 7, 3, 8, 8, 3, 5, 7, 1, 1, 7, 8, 7, 7, 3, 3, 7, 3, 3, 8, 7, 7, 7, 7, 7, 9, 8, 7, 5, 7, 7, 1, 1, 3, 3, 8, 7, 3, 5, 1, 3, 8, 5, 3, 5, 3, 1, 7, 1, 3, 7, 7, 9, 7, 9, 3, 3, 7, 7, 7, 7, 3, 7, 3, 9, 5, 9, 7, 3, 7, 8, 5, 9, 7, 9, 5, 5

Offset: 0

Roger L. Bagula, Jun 22 2002

All terms are in {1, 3, 5, 7, 8, 9}.

Ivars Peterson, The Jungles of Randomness, 1998, John Wiley and Sons, Inc., page 207.

Cf. A000040, A072003.

f[0]=f[1]=f[2]=f[3]=1; f[x_] := f[x]=f[x-1]+f[x-4]+Floor[f[x-1]/10+f[x-4]/10];
g[x_] := g[x]=9-Mod[f[x], 9];
h[x_] := h[x]=10-Mod[Prime[g[x]], 10];
Table[h[n], {n, 0, 200}];

a(n) = 10 - (prime(g(n)) mod 10) with g(n) = 9 - (f(n) mod 9) and f(n) = f(n-1) + f(n-4) + floor((f(n-1) + f(n-4))/10) for n>= 4, f(n) = 1 for n<4.

Edited by Robert G. Wilson v, Jun 25 2002

Edited by the Associate Editors of the OEIS, Jan 28 2022

A074879 10 - Mod(prime(n),10) when prime(n) + 22 = prime(n+1).

Original entry on oeis.org

1, 9, 9, 3, 1, 1, 1, 3, 3, 1, 3, 1, 3, 1, 1, 3, 1, 9, 1, 3, 1, 3, 1, 9, 1, 3, 9, 3, 9, 3, 3, 1, 9, 3, 1, 1, 3, 9, 9, 3, 3, 1, 1, 3, 9, 9, 1, 1, 3, 3, 1, 3, 3, 1, 1, 1, 9, 9, 1, 1, 9, 3, 1, 9, 1, 3, 1, 1, 9, 1, 1, 1, 3, 1, 3, 9, 9, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 9, 9, 1, 3, 9, 1, 3, 1, 9, 3, 1, 9, 9, 9, 1, 1, 1

Offset: 1

Roger L. Bagula, Sep 30 2002

Cf. A072003, A061779.

[10-(n mod 10): n in PrimesUpTo(50000) | n+22 eq NextPrime(n)];  // Bruno Berselli, Apr 12 2011

10 - Mod[ Prime[ Select[ Range[5220], Prime[ # ] + 22 == Prime[ # + 1] & ]], 10]
10-Mod[#,10]&/@Transpose[Select[Partition[Prime[Range[6000]],2,1], Last[#]- First[#]==22&]][[1]] (* Harvey P. Dale, Apr 12 2011 *)

Edited by Robert G. Wilson v and N. J. A. Sloane, Oct 03 2002

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A106727 Triangle T(n,k) = (f(n+1)*f(k+1) mod 10), where f(j) = 10 - (prime(j+3) mod 10), read by rows.

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A122754 a(n) = 10*n - A101306(n).

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A071641 a(n) defined by recursion in the formula section.

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A074879 10 - Mod(prime(n),10) when prime(n) + 22 = prime(n+1).

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