A228452 -id:A228452 - cp's OEIS frontend

A230699 Sequence of pairs k,g such that k2^n-1, k2^n-1+g, k2^n-1+2g, and k2^n+3g are four consecutive primes in arithmetic progression for the smallest odd k.

135, -6, 63, 6, 415, -6, 987, 6, 55, -6, 273, 6, 1195, -6, 299, 18, 1371, 6, 5, -6, 189, 6, 1077, 6, 7111, 6, 15, -6, 2821, -18, 15465, 24, 1081, 6, 11475, -6, 17155, -6, 3393, 12, 9751, 6, 16523, -24, 165, -6, 7395, -6, 8695, -6, 20325, -6, 7153, 18, 2235, -6

Offset: 1

Pierre CAMI, Oct 30 2013

sign

The number g may be negative.

g is always 0 mod 6 so a multiple of 6.

			135*2^1-1=269, 135*2^1-1-6=263, 135*2^1-1-2*6=257, 135*2^1-1-3*6=251
269, 263, 257, 251 are four consecutive primes in arithmetic progression so a(1)=135, a(2)=-6.
63*2^2-1=251, 63*2^2-1+6=257, 63*2^2-1+2*6=263, 63*2^2-1-3*6=269
251, 257, 263, 269 are four consecutive primes in arithmetic progression so a(3)=63 a(4)=6.

Pierre CAMI, Table of n, a(n) for n = 1..390

Cf. A227888, A228452, A228754.

A231576 Sequence of pairs k,g such that k is the smallest odd number and k2^n-1-g, k2^n-1, k*2^n-1+g are three consecutive primes in arithmetic progression.

Original entry on oeis.org

3, 2, 53, 12, 33, 6, 69, 6, 19, 6, 2193, 12, 93, 6, 113, 6, 87, 6, 413, 12, 1165, 12, 143, 6, 237, 6, 47, 6, 315, 18, 779, 6, 631, 30, 797, 6, 735, 12, 567, 18, 397, 6, 351, 24, 195, 18, 39, 36, 2719, 6, 971, 6, 1369, 30, 635, 18, 1501, 12, 593, 72, 2053, 6

Offset: 1

Pierre CAMI, Nov 11 2013

nonn

			3*2^1-1-2=3, 3*2^1-1=5, 3*2^1-1+2=7, so first pair = 3,2 (the only one with g=2).
53*2^2-1-12=199, 53*2^2-1=211, 53*2^2-1+12=223, so second pair = 53,12.

Pierre CAMI, Table of n, a(n) for n = 1..1300
Pierre CAMI, PFGW Script

Cf. A228452, A228454, A230699, A230852.

A228454 Gap g such that k2^n-1 , k2^n-1+g , k2^n-1+2g or k2^n-1-g , k2^n-1 , k*2^n-1+g are consecutive primes in arithmetic progression for the smallest prime k.

Original entry on oeis.org

2, 12, 6, 6, 6, 6, 24, 6, 6, 12, 6, 30, 18, 6, 18, 6, 30, 6, 6, 36, 6, 18, 36, 12, 6, 6, 6, 6, 6, 72, 6, 6, 6, 6, 6, 6, 18, 6, 6, 60, 6, 12, 6, 12, 18, 6, 18, 6, 30, 30, 60, 48, 78, 36, 54, 78, 36, 6, 6, 54, 6, 54, 12, 78, 6, 108, 108, 30, 6, 60, 24, 48, 18, 6, 42

Offset: 1

Pierre CAMI, Oct 27 2013

nonn

Primes k in A228452.

Pierre CAMI, Table of n, a(n) for n = 1..350

Cf. A228452.

cp's OEIS Frontend

A230699 Sequence of pairs k,g such that k2^n-1, k2^n-1+g, k2^n-1+2g, and k2^n+3g are four consecutive primes in arithmetic progression for the smallest odd k.

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A231576 Sequence of pairs k,g such that k is the smallest odd number and k2^n-1-g, k2^n-1, k*2^n-1+g are three consecutive primes in arithmetic progression.

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A228454 Gap g such that k2^n-1 , k2^n-1+g , k2^n-1+2g or k2^n-1-g , k2^n-1 , k*2^n-1+g are consecutive primes in arithmetic progression for the smallest prime k.

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cp's OEIS Frontend

A230699 Sequence of pairs k,g such that k*2^n-1, k*2^n-1+g, k*2^n-1+2*g, and k*2^n+3*g are four consecutive primes in arithmetic progression for the smallest odd k.

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A231576 Sequence of pairs k,g such that k is the smallest odd number and k*2^n-1-g, k*2^n-1, k*2^n-1+g are three consecutive primes in arithmetic progression.

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A228454 Gap g such that k*2^n-1 , k*2^n-1+g , k*2^n-1+2*g or k*2^n-1-g , k*2^n-1 , k*2^n-1+g are consecutive primes in arithmetic progression for the smallest prime k.

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A230699 Sequence of pairs k,g such that k2^n-1, k2^n-1+g, k2^n-1+2g, and k2^n+3g are four consecutive primes in arithmetic progression for the smallest odd k.

A231576 Sequence of pairs k,g such that k is the smallest odd number and k2^n-1-g, k2^n-1, k*2^n-1+g are three consecutive primes in arithmetic progression.

A228454 Gap g such that k2^n-1 , k2^n-1+g , k2^n-1+2g or k2^n-1-g , k2^n-1 , k*2^n-1+g are consecutive primes in arithmetic progression for the smallest prime k.