A286816
Smallest b such that the k consecutive primes starting with prime(n) are all base-b Wieferich primes, i.e., satisfy b^(p-1) == 1 (mod p^2). Square array A(n, k), read by antidiagonals downwards.
Original entry on oeis.org
5, 17, 8, 449, 26, 7, 557, 226, 18, 18, 19601, 1207, 1207, 148, 3, 132857, 54568, 1451, 606, 239, 19, 4486949, 2006776, 13543, 13543, 3469, 249, 38, 126664001, 20950343, 296449, 296449, 24675, 653, 423, 28, 2363321449, 230695118, 23250274, 17134811, 3414284, 39016, 5649, 28, 28, 5229752849, 5229752849, 882345432, 741652533, 36763941, 14380864, 217682, 26645, 63, 14
Offset: 1
The sequence of base-226 Wieferich primes starts 3, 5, 7, 97, 157, ... Since 226 is the smallest b such that the three consecutive primes starting with prime(2) = 3 are base-b Wieferich primes, A(2, 3) = 226.
Array starts:
n=1: 5, 17, 449, 557, 19601, 132857
n=2: 8, 26, 226, 1207, 54568, 2006776
n=3: 7, 18, 1207, 1451, 13543, 296449
n=4: 18, 148, 606, 13543, 296449, 17134811
n=5: 3, 239, 3469, 24675, 3414284, 36763941
n=6: 19, 249, 653, 39016, 14380864, 34998229
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primevec(initialp, vecsize) = my(v=[initialp]); while(#v < vecsize, v=concat(v, nextprime(v[#v]+1))); v
a(n, k) = my(v=primevec(prime(n), k), b=2, i=0); while(1, for(x=1, #v, if(Mod(b, v[x]^2)^(v[x]-1)!=1, i++; break)); if(i==0, return(b)); b++; i=0)
array(rows, cols) = for(s=1, rows, for(t=1, cols, print1(a(s, t), ", ")); print(""))
array(5, 6) \\ print 5 X 6 array
A344828
a(n) is the smallest b > 1 such that prime(n), prime(n+1), prime(n+2) and prime(n+3) are all base-b Wieferich primes.
Original entry on oeis.org
557, 1207, 1451, 13543, 24675, 39016, 217682, 165407, 1357748, 399254, 1146590, 325346, 1895206, 3365181, 4674177, 21251205, 40698745, 6795147, 36463448, 12717474, 54383927, 7411274, 35989426, 101112784, 86045167, 13128506, 276293632, 169093089, 223680564, 137073637
Offset: 1
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a(n) = my(v=[prime(n)]); while(#v < 4, v=concat(v, nextprime(v[#v]+1))); for(b=2, oo, for(k=1, #v, if(Mod(b, v[k]^2)^(v[k]-1)!=1, break, if(k==#v, return(b)))))
A344830
a(n) is the smallest b > 1 such that prime(n), prime(n+1), prime(n+2), prime(n+3), prime(n+4) and prime(n+5) are all base-b Wieferich primes.
Original entry on oeis.org
132857, 2006776, 296449, 17134811, 36763941, 34998229, 31239565, 968576295, 1027038511, 287811239, 15022368222, 33452659960, 19477999997, 132892045949, 47341045210, 32176849766, 106967760951, 303459122992, 20216391690, 1411108384416, 219517083156, 361244580521, 455588981749
Offset: 1
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a(n) = my(v=[prime(n)]); while(#v < 6, v=concat(v, nextprime(v[#v]+1))); for(b=2, oo, for(k=1, #v, if(Mod(b, v[k]^2)^(v[k]-1)!=1, break, if(k==#v, return(b)))))
A344831
a(n) is the smallest b > 1 such that prime(n), prime(n+1), prime(n+2), prime(n+3), prime(n+4), prime(n+5) and prime(n+6) are all base-b Wieferich primes.
Original entry on oeis.org
4486949, 20950343, 23250274, 741652533, 710808570, 2380570527, 4967352848, 39489360341, 6143373023, 64470545267, 627069771908, 407165268367, 676579634125, 676579634125, 2923957743077, 369072416795, 5110842013966, 19645397150616, 16037329738682, 5867065121893, 31015370285102
Offset: 1
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a(n) = my(v=[prime(n)]); while(#v < 7, v=concat(v, nextprime(v[#v]+1))); for(b=2, oo, for(k=1, #v, if(Mod(b, v[k]^2)^(v[k]-1)!=1, break, if(k==#v, return(b)))))
A344832
a(n) is the smallest b > 1 such that prime(n), prime(n+1), prime(n+2), prime(n+3), prime(n+4), prime(n+5), prime(n+6) and prime(n+7) are all base-b Wieferich primes.
Original entry on oeis.org
126664001, 230695118, 882345432, 12106746963, 93732236423, 66888229817, 84391291750, 3685694924698, 4506100208066, 1058174730735, 3827951700972, 58674393094169, 676579634125, 83450880181400, 100819901293157, 365919682326848, 695001153578920, 1046021079620904, 2989564836636529, 3724954519064878
Offset: 1
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a(n) = my(v=[prime(n)]); while(#v < 8, v=concat(v, nextprime(v[#v]+1))); for(b=2, oo, for(k=1, #v, if(Mod(b, v[k]^2)^(v[k]-1)!=1, break, if(k==#v, return(b)))))
A344827
a(n) is the smallest b > 1 such that prime(n), prime(n+1) and prime(n+2) are all base-b Wieferich primes.
Original entry on oeis.org
449, 226, 1207, 606, 3469, 653, 5649, 26645, 7805, 6154, 36088, 14368, 49662, 66565, 153463, 40667, 760637, 31871, 265418, 411467, 484205, 148989, 688285, 796095, 1920186, 747071, 3516680, 569812, 905979, 3193580, 3303343, 1967646, 1728157, 4436267, 912246
Offset: 1
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a(n) = my(v=[prime(n)]); while(#v < 3, v=concat(v, nextprime(v[#v]+1))); for(b=2, oo, for(k=1, #v, if(Mod(b, v[k]^2)^(v[k]-1)!=1, break, if(k==#v, return(b)))))
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