A279021
Triangle read by rows, giving the arithmetic progressions of prime-indexed primes in A278735.
Original entry on oeis.org
3, 3, 5, 5, 11, 17, 353, 431, 509, 587, 13297, 21937, 30577, 39217, 47857, 1561423, 2716423, 3871423, 5026423, 6181423, 7336423, 291461857, 373881397, 456300937, 538720477, 621140017, 703559557, 785979097
Offset: 1
a(7) = 353, a(8) = 431, a(9) = 509, and a(10) = 587 because 353 = prime(prime(20)), 431 = prime(prime(23)), 509 = prime(prime(25)), 587 = prime(prime(28)), and 431-353 = 509-431 = 587-509 = 78.
The triangle begins:
3;
3, 5;
5, 11, 17;
353, 431, 509, 587;
13297, 21937, 30577, 39217, 47857;
1561423, 2716423, 3871423, 5026423, 6181423, 7336423;
...
A274825
Gaps associated with the arithmetic progressions in A278735.
Original entry on oeis.org
0, 2, 6, 78, 8640, 1155000, 82419540
Offset: 1
a(4) = 78 because 353 = prime(prime(20)), 431 = prime(prime(23)), 509 = prime(prime(25)), 587 = prime(prime(28)), and 431-353 = 509-431 = 587-509 = 78.
For the corresponding arithmetic progressions, see _Charles R Greathouse IV_'s example in A278735. - _Bobby Jacobs_, Jan 02 2017
A278735
Smallest prime-indexed prime ending an arithmetic progression of n prime-indexed primes.
Original entry on oeis.org
3, 5, 17, 587, 47857, 7336423, 785979097
Offset: 1
a(4) = 587 because 353 = prime(prime(20)), 431 = prime(prime(23)), 509 = prime(prime(25)), 587 = prime(prime(28)), and 431-353 = 509-431 = 587-509 = 78.
From _Charles R Greathouse IV_, Nov 27 2016: (Start)
The corresponding arithmetic progressions are
3;
3, 5;
5, 11, 17;
353, 431, 509, 587;
13297, 21937, 30577, 39217, 47857;
1561423, 2716423, 3871423, 5026423, 6181423, 7336423;
and with the main diagonal being terms of this sequence. (End)
-
findAP(len)=my(t); if(len<3, return(v[len])); for(i=len, #v, for(j=1, i-len+1, t=(v[i]-v[j])/(len-1); if(denominator(t)>1, next); forstep(k=v[j]+t, v[i]-t, t, if(!setsearch(v, k), next(2))); return(vector(len, k, v[j]+(k-1)*t)))); "not found"
listPIP(lim)=my(v=List(), p); forprime(q=2, lim, if(isprime(p++), listput(v, q))); Vec(v)
v=listPIP(1e7);
apply(findAP, [1..6]) \\ Charles R Greathouse IV, Nov 27 2016
A279062
Initial terms of the arithmetic progressions in A278735.
Original entry on oeis.org
3, 3, 5, 353, 13297, 1561423, 291461857
Offset: 1
a(4) = 353 because 353 = prime(prime(20)), 431 = prime(prime(23)), 509 = prime(prime(25)), 587 = prime(prime(28)), and 431-353 = 509-431 = 587-509 = 78.
The corresponding arithmetic progressions are
3;
3, 5;
5, 11, 17;
353, 431, 509, 587;
13297, 21937, 30577, 39217, 47857;
1561423, 2716423, 3871423, 5026423, 6181423, 7336423;
...
Showing 1-4 of 4 results.
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