A227888 -id:A227888 - cp's OEIS frontend

A228452 Smallest prime k such that k2^n-1 , k2^n-1+2j , k2^n-1+4j or k2^n-1-2j , k2^n-1 , k2^n-1+2j are consecutive primes in arithmetic progression for some j.

3, 53, 19, 3, 19, 593, 313, 113, 1699, 1163, 31, 4217, 31, 47, 7993, 1013, 631, 347, 3793, 3923, 397, 353, 2551, 83, 2719, 971, 3709, 6827, 6361, 593, 2053, 16073, 2719, 2753, 4441, 8663, 31, 131, 61, 5867, 379, 587, 9631, 1907, 8581, 23, 15739, 4049, 2281

Offset: 1

Pierre CAMI, Oct 27 2013

nonn

			53*2^2-1-12=199, 53*2^2-1=211 and 53*2^2-1+12=223, so a(2)=53.
19*2^3-1=151, 19*2^3-1+6=157 and 19*2^3-1+12=163, so a(3)=19.

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

Cf. A227888.

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.

Original entry on oeis.org

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.

cp's OEIS Frontend

A228452 Smallest prime k such that k2^n-1 , k2^n-1+2j , k2^n-1+4j or k2^n-1-2j , k2^n-1 , k2^n-1+2j are consecutive primes in arithmetic progression for some j.

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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.

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cp's OEIS Frontend

A228452 Smallest prime k such that k*2^n-1 , k*2^n-1+2*j , k*2^n-1+4*j or k*2^n-1-2*j , k*2^n-1 , k*2^n-1+2*j are consecutive primes in arithmetic progression for some j.

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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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A228452 Smallest prime k such that k2^n-1 , k2^n-1+2j , k2^n-1+4j or k2^n-1-2j , k2^n-1 , k2^n-1+2j are consecutive primes in arithmetic progression for some j.

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.