A163681
Smaller prime p in Ormiston pairs (p, q) with q - p = 72.
Original entry on oeis.org
1290719, 1477219, 1802419, 2520697, 2902519, 3327419, 3391697, 3498119, 4596419, 4641919, 4709519, 5521819, 5835619, 6091031, 6267419, 6642919, 6943919, 7118519, 7480519, 8241019, 8630519, 8934319, 8946919, 9859697
Offset: 1
(1802419, 1802491) is an Ormiston pair with gap 72, so 1802419 is in the sequence.
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[ p: p in PrimesUpTo(10000000) | q-p eq 72 and a eq b where a is Sort(Intseq(p)) where b is Sort(Intseq(q)) where q is NextPrime(p) ];
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Transpose[Select[Select[Partition[Prime[Range[800000]],2,1],Last[#]-First[#]==72&],Sort[IntegerDigits[First[#]]]==Sort[IntegerDigits[Last[#]]]&]][[1]] (* Harvey P. Dale, Feb 14 2011 *)
A217372
Initial prime in the first Ormiston n-tuple.
Original entry on oeis.org
2, 1913, 11117123, 6607882123, 20847942560791
Offset: 1
(1913, 1931) is the first case of two consecutive primes with the same digits. The first 3-, 4- and 5-tuples are: (11117123, 11117213, 11117321), (6607882123, 6607882213, 6607882231, 6607882321), (20847942560791, 20847942560917, 20847942560971, 20847942561079, 20847942561097).
A228135
Smaller of two consecutive semiprimes which are anagrams of each other.
Original entry on oeis.org
278, 1945, 2545, 4045, 5389, 9134, 9289, 12634, 17678, 23578, 25034, 25178, 27289, 32245, 32689, 34889, 35078, 40234, 42289, 47578, 47789, 48979, 50579, 51434, 51589, 55534, 55634, 55934, 57289, 57779, 69334, 69478, 70178, 70234, 71945, 71989, 72134, 76345
Offset: 1
278 and 287 are two successive semiprimes.
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with(numtheory):T:=array(1..50000):k:=0:for i from 1 to 200000 do:if bigomega(i)=2 then k:=k+1:T[k]:=i:else fi:od:for n from 1 to k-1 do:p1:=T[n]:p2:= T[n+1]:pp1:=convert(p1,base,10): pp2:=convert(p2,base,10):n1:=sort(pp1):n2:=sort(pp2): if n1=n2 then printf(`%d, `,p1):else fi:od:
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range[n_Integer]:=Select[Range@n,PrimeOmega@#==2&];
anagramQ[l_List]:=(l1=Sort@#&/@IntegerDigits@l;l1[[1]]==l1[[2]]);
Select[Partition[range@100000,2,1],anagramQ]\[Transpose]//First (* Hans Rudolf Widmer, Oct 06 2021 *)
A156117
Smaller of two successive primes using the same digits such that the hundreds digit is the most significant digit to differ.
Original entry on oeis.org
48091, 64091, 116293, 139091, 145091, 162091, 244091, 250091, 276781, 321091, 359783, 456293, 558091, 623071, 666091, 684091, 708091, 771091, 810091, 831091, 836071, 873091, 877091, 897781, 939091, 1032071, 1041091, 1065091, 1087091
Offset: 1
18379 is not included since the next prime 18397 does not change the hundreds digit even though the same digits are used.
64091 is included because the next prime is 64109 which uses the same digits and the hundreds digit is the most significant digit changed.
29610901 is not included because the next prime is 29611009 which differs in the thousands digit.
Cf.
A069567 properly contains this sequence.
A337784
Smaller of two consecutive oblong numbers which are anagrams of each other.
Original entry on oeis.org
23256, 530712, 809100, 11692980, 17812620, 20245500, 22834062, 23527350, 29154600, 83768256, 182236500, 189847062, 506227500, 600127506, 992218500, 1363566402, 1640209500, 2175895962, 2422657620, 2477899062, 2520190602, 3041687952, 3764129256, 4760103042
Offset: 1
530712 is in the sequence because it is an oblong number, 530712 = 728 * 729, and the next oblong number, 532170 = 729 * 730, is an anagram of 530712.
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s = {}; o1 = 1; d1 = Sort @ IntegerDigits[o1]; Do[o2 = n*(n + 1); d2 = Sort @ IntegerDigits[o2]; If[d2 == d1, AppendTo[s, o1]]; o1 = o2; d1 = d2, {n, 2, 70000}]; s (* Amiram Eldar, Sep 21 2020 *)
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ok(k) = {my(b, m=0); if(issquare(4*k + 1), b=truncate(sqrt(4*k + 1) - 1)/2; if(vecsort(digits(k)) == vecsort(digits((b + 1)*(b + 2))), m = 1)); m}
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