A084758
The slowest increasing sequence of primes such that difference of successive terms is unique.
Original entry on oeis.org
2, 3, 5, 11, 19, 23, 37, 47, 59, 79, 97, 113, 137, 163, 191, 223, 257, 293, 331, 353, 383, 431, 487, 541, 587, 631, 673, 733, 773, 823, 881, 947, 1009, 1061, 1129, 1193, 1277, 1367, 1439, 1531, 1601, 1697, 1777, 1871, 1949, 2053, 2129, 2203, 2309, 2411, 2521
Offset: 1
Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 17 2003
After 23, the next term is 37 and not 29 or 31 as 29-23= 11-5 =6, 31-23 = 19-11=8.
-
diffs = {}; prms = {2}; p = 2; Do[While[p = NextPrime[p]; d = p - prms[[-1]]; MemberQ[diffs, d]]; AppendTo[diffs, d]; AppendTo[prms, p], {100}]; prms (* T. D. Noe, Nov 01 2011 *)
A121861
Least previously nonoccurring positive integer such that partial sum + 1 is prime.
Original entry on oeis.org
1, 3, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, 28, 20, 34, 36, 42, 44, 46, 62, 52, 38, 60, 48, 58, 56, 54, 40, 50, 64, 68, 72, 76, 84, 66, 96, 74, 70, 80, 100, 86, 78, 88, 104, 90, 106, 122, 112, 98, 102, 94, 92, 118, 114, 108, 110, 124, 116, 138, 82, 120, 128, 150
Offset: 1
a(1) = 1 because 1+1 = 2 is prime.
a(2) = 3 because 1+3+1 = 5 is prime.
a(3) = 2 because 1+3+2+1 = 7 is prime.
a(4) = 4 because 1+3+2+4+1 = 11 is prime.
-
N:= 200: # to get all terms before the first term > N
A[1]:= 1: A[2]:= 3: P:= 5; S:= [seq(2*i,i=1..N/2)]:
for n from 3 while assigned(A[n-1]) do
for k from 1 to nops(S) do
if isprime(P+S[k]) then
A[n]:= S[k];
P:= P + S[k];
S:= subsop(k=NULL,S);
break
fi
od;
od:
seq(A[i],i=1..n-2); # Robert Israel, May 02 2017
-
f[s_] := Append[s, k = 1; p = 1 + Plus @@ s; While[MemberQ[s, k] || ! PrimeQ[p + k], k++ ]; k]; Nest[f, {}, 67] (* Robert G. Wilson v *)
A122866
Consider the array of sequences defined to be "the least previously nonoccurring positive integer such that partial sum + k is prime" beginning with k=0. This sequence is the main diagonal of that array.
Original entry on oeis.org
2, 3, 6, 4, 12, 10, 16, 12, 16, 24, 26, 24, 30, 28, 28, 44, 36, 42, 20, 38, 34, 54, 54, 56, 48, 44, 50, 52, 68, 56, 56, 60, 62, 66, 66, 70, 76, 84, 76, 58, 92, 90, 88, 90, 80, 88, 92, 102, 104, 102, 114, 104, 108, 98, 114, 108, 92, 100, 120, 126, 124, 130, 126, 142, 116, 126
Offset: 0
The array of sequences begins
k= 0: 2, 1, 4, 6, 10, 8, 12, 16, 14, 24, 30, 22, 18, 26, 34, ...,.
k= 1: 1, 3, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, ...,.
k= 2: 1, 2, 6, 8, 4, 14, 10, 12, 20, 18, 16, 24, 26, 28, 32, ...,.
k= 3: 2, 6, 8, 4, 14, 10, 12, 20, 18, 16, 24, 26, 28, 32, 34, ...,.
k= 4: 1, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, ...,.
k= 5: 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, 28, ...,.
-
f[s_] := Append[s, k = 1; p = q + Plus @@ s; While[MemberQ[s, k] || !PrimeQ[p + k], k++ ]; k]; T[n_, k_] := Nest[q = k; f, {}, n][[ -1]]; Table[T[n, n - 1], {n, 66}]
A122867
Consider the array of sequences defined to be "the least previously nonoccurring positive integer such that partial sum + k is prime" beginning with k=0. This sequence is that array read by successive antidiagonals.
Original entry on oeis.org
2, 1, 1, 1, 3, 4, 2, 2, 2, 6, 1, 6, 6, 4, 10, 2, 2, 8, 8, 6, 8, 1, 4, 4, 4, 4, 12, 12, 4, 4, 6, 6, 14, 14, 8, 16, 3, 2, 2, 12, 12, 10, 10, 10, 14, 2, 2, 6, 6, 8, 8, 12, 12, 14, 24, 1, 6, 4, 10, 10, 10, 10, 20, 20, 18, 30, 2, 2, 12, 6, 8, 8, 14, 14, 18, 18, 22, 22, 1, 4, 4, 8, 8, 16, 16, 18, 18, 16
Offset: 1
The array of sequences begins
k= 0: 2, 1, 4, 6, 10, 8, 12, 16, 14, 24, 30, 22, 18, 26, 34, ...,.
k= 1: 1, 3, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, ...,.
k= 2: 1, 2, 6, 8, 4, 14, 10, 12, 20, 18, 16, 24, 26, 28, 32, ...,.
k= 3: 2, 6, 8, 4, 14, 10, 12, 20, 18, 16, 24, 26, 28, 32, 34, ...,.
k= 4: 1, 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, ...,.
k= 5: 2, 4, 6, 12, 8, 10, 14, 18, 22, 26, 24, 16, 30, 32, 28, ...,.
-
f[s_] := Append[s, k = 1; p = q + Plus @@ s; While[MemberQ[s, k] || !PrimeQ[p + k], k++ ]; k]; T[n_, k_] := Nest[q = k; f, {}, n][[ -1]]; Table[T[k, n - k], {n, 13}, {k, n}] // Flatten
Showing 1-4 of 4 results.
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